2023 |
Panyushev D., Combinatorial and geometric constructions associated with the Kostant cascade,
J. Lie Theory, 33, no. 2 (2023), 497--526 http://iitp.ru/https://www.heldermann.de/JLT/JLT33/JLT332/jlt33021.htm
|
Panyushev D., Yakimova O., Automorphisms of finite order, periodic contractions,
and Poisson-commutative subalgebras of S(g),
Math. Zeitschrift, 303, no. 2 (2023), Article 51. http://iitp.ru/https://doi.org/10.1007/s00209-022-03199-x
|
2022 |
Panyushev D., Yakimova O., Reductive subalgebras of semisimple Lie algebras and Poisson commutativity,
J. Symplectic Geom., 20 no. 4 (2022), 911--926 http://iitp.ru/https://dx.doi.org/10.4310/JSG.2022.v20.n4.a4
|
2021 |
Panyushev D., Yakimova O., Poisson-commutative subalgebras of S(g) associated with involutions,
Intern. Math. Res. Notices, 2021, no. 23, 18367--18406. http://iitp.ru/https://doi.org/10.1093/imrn/rnaa041
|
Panyushev D., Yakimova O., Periodic automorphisms, compatible Poisson brackets, and Gaudin subalgebras,
Transform. Groups, 26, no. 2 (2021), 641--670 http://iitp.ru/https://doi.org/10.1007/S00031-021-09650-3
|
Panyushev D., Yakimova O., Compatible Poisson brackets associated with 2-splittings and Poisson commutative subalgebras of
S(g), J. London Math. Soc., 103, no. 4 (2021), 1577--1595. http://iitp.ru/https://doi.org/10.1112/jlms.12418
|
Panyushev D., Nilpotent orbits and mixed gradings of semisimple Lie algebras, Indagationes Mathematicae, 32, no. 5 (2021), 1095-1114 http://iitp.ru/https://doi.org/10.1016/j.indag.2021.01.007
|
2020 |
Panyushev D., Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications,
Advances in Math., 374 (2020), Article 107390 http://iitp.ru/https://doi.org/10.1016/j.aim.2020.107390
|
Panyushev D., Yakimova O., Takiff algebras with polynomial rings of symmetric invariants,
Transformation Groups, 25, no.2 (2020), 609--624 http://iitp.ru/https://doi.org/10.1007/s00031-019-09532-9
|
Panyushev D., Yakimova O., Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and
flag varieties, Math. Zeitschrift, 295 (2020), 101-127. http://iitp.ru/https://doi.org/10.1007/s00209-019-02357-y
|
Panyushev D., Glorious pairs of roots and abelian ideals of a Borel subalgebra,
J. Algebraic Combinatorics, 52 (2020), 505-525 http://iitp.ru/https://doi.org/10.1007/s10801-019-00911-9
|
Panyushev D., Abelian ideals of a Borel subalgebra and root systems, II,
Algebras and Representation Theory, 23, no.4 (2020), 1487-1498 http://iitp.ru/https://doi.org/10.1007/s10468-019-09902-7
|
2019 |
Panyushev D., Yakimova O., Semi-direct products involving Sp_{2n} or Spin_n with free algebras of symmetric invariants,
In: M. Gorelik, V. Hinich, A. Melnikov (Eds.):
``Representations and Nilpotent Orbits of Lie Algebraic Systems: In Honour of the 75th Birthday of Tony Joseph"", Progress in Math. 330,
Basel Birkhäuser 2019, 441-470. http://iitp.ru/https://doi.org/10.1007/978-3-030-23531-4_12
|
Panyushev D., Yakimova O., Nilpotent subspaces and nilpotent orbits, J. Austral. Math. Soc., 106 (2019), 104-126 http://iitp.ru/https://doi.org/10.1017/S1446788718000071
|
2018 |
Panyushev D., Yakimova O.S., On seaweed subalgebras and meander graphs in type D,
J. Pure Applied Algebra, 222, no. 11 (2018), 3414-3431 http://iitp.ru/https://doi.org/10.1016/j.jpaa.2017.12.015
|
2017 |
Panyushev D., Yakimova O.S., Symmetric invariants related to representations of exceptional simple groups,
Òðóäû Ìîñê. Ìàòåì. Îá-âà, ò.78 (2017), âûï. 2, ñ.195--207 http://mi.mathnet.ru/mmo597
|
Panyushev D., Abelian ideals and amazing roots, Intern. J. Math., 28, no. 14 (2017),
1750105 (9 pages) http://iitp.ru/https://doi.org/10.1142/S0129167X17501051
|
Panyushev D., Yakimova O., Semi-direct products of Lie algebras and covariants, J. Algebra,
290 (2017), 283-315. http://iitp.ru/https://doi.org/10.1016/j.jalgebra.2017.06.036
|
Panyushev D., On the orbits of a Borel subgroup in abelian ideals,
Transformation Groups, 22, no.2 (2017), 503-524. http://iitp.ru/https://dx.doi.org/10.1007/s00031-016-9391-8
|
2016 |
Panyushev D., Yakimova O.S., On seaweed subalgebras and meander graphs in type C,
Pacific J. Math., 285, no.2 (2016), 485--499. http://dx.doi.org/10.2140/pjm.2016.285.485
|
Panyushev D., On Lusztig’s q-analogues of all weight multiplicities of a representation,
In: W. Ballmann, C. Blohmann, G. Faltings, P. Teichner, D. Zagier (Eds.): ``Arbeitstagung Bonn 2013. In
Memory of Friedrich Hirzebruch", Progr. Math. 319, Birkhäuser 2016, 289-305. http://iitp.ru/https://dx.doi.org/10.1007/978-3-319-43648-7_10
|
Panyushev D., Weight posets associated with gradings of simple Lie algebras, Weyl groups, and arrangements of hyperplanes, J. Algebraic Combinatorics, 44, no. 2 (2016), 325--344. http://dx.doi.org/10.1007/s10801-016-0671-0
|
Panyushev D., Normalisers of abelian ideals of Borel subalgebras and Z-gradings of a simple Lie algebra, J. Lie Theory, 26 (2016), 659-672. http://www.heldermann.de/JLT/JLT26/JLT263/jlt26027.htm
|
Panyushev D., Minimal inversion complete sets and maximal abelian ideals,
J. Algebra, 445 (2016), 163-180. http://iitp.ru/https://dx.doi.org/10.1016/j.jalgebra.2015.08.016
|
2015 |
Panyushev D., Antichains in weight posets associated with gradings of simple Lie algebras,
Math. Zeitschrift, 281, no.3-4 (2015), 1191-1214. http://link.springer.com/article/10.1007/s00209-015-1527-3
|
Panyushev D., The Dynkin index and sl2-subalgebras of simple Lie algebras,
J. Algebra, 430 (2015), 15-25. http://dx.doi.org/10.1016/j.jalgebra.2015.01.033
|
2014 |
Panyushev D., Abelian ideals of a Borel subalgebra and root systems, J. European Math. Soc., 16, no.12 (2014), 2693-2708. http://dx.doi.org/10.4171/JEMS/496
|
Panyushev D., Yakimova O.S., On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple
Lie algebras, Bull. Sci. Math., 138, no.6 (2014), 705-720. http://dx.doi.org/10.1016/j.bulsci.2013.11.004
|
Panyushev D., Wide subalgebras of semisimple Lie algebras,
Algebras and Representation Theory, 17, no.3 (2014), 931-944. http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s10468-013-9425-z
|
2013 |
Panyushev D., Commuting involutions of Lie algebras, commuting varieties, and simple Jordan algebras, Algebra and Number Theory, 7, no.6 (2013), 1505-1534. http://dx.doi.org/10.2140/ant.2013.7.1505
|
Panyushev D., Yakimova O.S., Parabolic contractions of semisimple Lie algebras and their invariants,
Selecta Math. (New Series), 19, no.3 (2013), 699-717. http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00029-013-0122-x
|
Panyushev D., Commuting involutions and degenerations of isotropy representations, Transformation Groups, 8, no.2 (2013), 507-537. http://dx.doi.org/10.1007/s00031-013-9224-y
|
2012 |
Panyushev D., Yakimova O.S., On a remarkable contraction of semisimple Lie algebras,
Ann. Inst. Fourier, 62, no.6 (2012), 2053-2068. http://dx.doi.org/10.5802/aif.2742
|
Panyushev D., Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals,
Journal of Combinatorics, 3 (2012), 63-89. http://dx.doi.org/10.4310/JOC.2012.v3.n1.a3
|
Panyushev D., Quotients by actions of the derived group of a maximal unipotent subgroup,
Pacific Journal of Mathematics, 256 (2012), 381-405. http://dx.doi.org/10.2140/pjm.2012.256.381
|
Panyushev D., Invariant theory of little adjoint modules, J. Lie Theory,
22 (2012), 803-816.
|
Panyushev D., Invariants of a maximal unipotent subgroup and equidimensionality,
Bulletin des sciences mathématiques 136 (2012), 149-161. http://dx.doi.org/10.1016/j.bulsci.2011.11.006
|
2011 |
Panyushev D., Abelian ideals of a Borel subalgebra and subsets of the Dynkin diagram,
J. Algebra, 344 (2011), 197-204. http://dx.doi.org/10.1016/j.jalgebra.2011.07.012
|
Panyushev D., Fredman’s reciprocity, invariants of abelian groups, and the
permanent of the Cayley table, J. Algebraic Combin., 33 (2011),
111-125. http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s10801-010-0236-6
|
2010 |
Panyushev D., E.B.Vinberg, The work of Vladimir Morozov on Lie algebras,
Transformation Groups, 15 (2010), 1001-1013. http://iitp.ru/ http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00031-010-9097-2
|
Panyushev D., On divisible weighted Dynkin diagrams and reachable elements,
Transformation Groups, 15 (2010), 983-999. http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00031-010-9098-1
|
Panyushev D., Generalised Kostka-Foulkes polynomials and cohomology of line bundles on
homogeneous vector bundles, Selecta Math. (New Ser)., 16 (2010), 315–342. http://iitp.ru/ http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00029-010-0022-2
|
Panyushev D., Actions of the derived group of a maximal unipotent subgroup on $G$-varieties,
Intern. Math. Res. Notices 2010, no. 4 (2010), 674-700.
|
2009 |
Panyushev D., Properties of weight posets for weight multiplicity free representations,
Moscow Math. J. , 9, no. 4 (2009), 867--883.
|
Panyushev D., On the Dynkin index of a principal sl(2)-subalgebra,
Adv. Math., 221, no.4 (2009), 1115-1121.
|
Panyushev D., Periodic automorphisms of Takiff algebras, contractions, and θ-groups, Transformation Groups, 14 , no.2 (2009),
463-482.
|
Panyushev D., On orbits of antichains of positive roots, Europ. J.
Combinatorics, 30, no.2 (2009), 586-594.
|
2008 |
Panyushev D., Adjoint vector fields and differential operators on representation
spaces, Bull. London Math. Soc., 40, no.6 (2008),
1045-1064.
|
Panyushev D., Yakimova O.S., The argument shift method and maximal commutative subalgebras of
Poisson algebras,
Math. Res. Letters, 15 (2008), 239-249.
|
Panyushev D., Two results on centralisers of nilpotent elements,
J. Pure Applied Algebra 212 (2008), 774-779.
|
2007 |
Panyushev D., Yakimova O.S., Symmetric pairs and associated commuting varieties,
Math. Proc. Cambr. Phil. Soc. 143 (2007), 307-321.
|
Panyushev D., Premet A., Yakimova O., On symmetric invariants of centralisers in reductive Lie algebras,
J. Algebra, 313 (2007), 343-391.
|
Panyushev D., On the coadjoint representation of Z2-contractions of
reductive Lie algebras, Adv. Math., 213 (2007), 380-404.
|
Panyushev D., Semi-direct products of Lie algebras, their invariants and
representations, Publ. RIMS 43, no.4 (2007), 1199-1257.
|
2006 |
Panyushev D., Commutative subalgebras and sphericity in Z2-graded
Lie algebras,
Bull. London Math. Soc., 38, Part 5 (2006), 753-763.
|
Panyushev D., Yakimova O.S., The index of representations associated with stabilisers,
J. Algebra, 302 (2006), 280-304.
|
Panyushev D., The poset of positive roots and its relatives,
J. Alg. Combinatorics 23 (2006), 79-101.
|
Panyushev D., Normalizers of ad-nilpotent ideals,
Europ. J. Combinatorics 27 (2006), 153-178.
|
2005 |
Panyushev D., Ideals of Heisenberg type and minimax elements of affine Weyl
groups, in: Amer. Math. Soc. Transl., Series 2.
"Lie Groups and Invariant Theory" (E.B.Vinberg, Ed.) 213 (2005),
191-213.
|
Panyushev D., An extension of Rais’ theorem
and seaweed subalgebras of simple Lie algebras,
Annales Inst. Fourier 55 (2005), no. 3, 693-715.
|
Panyushev D., G.Röhrle, On spherical ideals of Borel subalgebras,
Archiv der Math. 84 (2005), 225-232.
|
Panyushev D., On Invariant Theory of θ-groups,
J. Algebra 283 (2005), 655-670.
|
2004 |
Panyushev D., On reachable elements and the boundary of nilpotent orbits in simple
Lie algebras, Bull. Sci. Math. 128 (2004), 859-870.
|
Panyushev D., Long Abelian ideals,
Adv. Math. 186 (2004), 307-316.
|
Panyushev D., Weight multiplicity free representations, $frak g$-endomorphism algebras,
and Dynkin polynomials, J. London Math. Soc.
69, Part 2 (2004), 273-290.
|
Panyushev D., Regions in the dominant chamber and nilpotent orbits,
Bull. Sci. Math.
128 (2004), 1-6.
|
Panyushev D., Short antichains in root systems, semi-Catalan arrangements,
and B-stable subspaces, Europ. J. Combinatorics
25 (2004), 93-112.
|
Panyushev D., AD-nilpotent ideals of a Borel subalgebra: generators and duality, J. Algebra 274 (2004),
822-846.
|
2003 |
Panyushev D., Some amazing properties of spherical nilpotent orbits,
Math. Zeitschrift, 245 (2003), 557–580.
|
Panyushev D., Abelian ideals of a Borel subalgebra and long positive roots, Intern. Math. Res. Notices, no. 35 (2003), 1889-1913.
|
Panyushev D., The index of a Lie algebra, the centraliser of a
nilpotent element, and the normaliser of the centraliser,
Math. Proc. Cambridge Phil. Soc. 134 (2003), 41-59.
|
2002 |
Akhiezer D., Panyushev D., Multiplicities in the branching rules and the complexity of homogeneous spaces, Moscow Math. Journal, 2
(2002), 17–33.
|
Panyushev D., On covariants of reductive algebraic groups,
Indagationes Math. 13 (2002), 125-129.
|
2001 |
Panyushev D., Inductive formulas for the index of seaweed Lie algebras,
Moscow Math. J. 1 (2001), 221-241.
|
Panyushev D., G.Röhrle, Spherical orbits and abelian ideals, Adv. in Math. 159 (2001), 229-246.
|
Panyushev D., Isotropy representations, eigenvalues of a
Casimir element, and commutative Lie subalgebras,
J. London Math. Soc. 64 (2001), 61-80.
|
Panyushev D., The exterior algebra and `Spin’ of an orthogonal $frak g$-module, Transformation Groups 6(2001), 371-396.
|
Panyushev D., Nilpotent pairs, dual pairs, and sheets,
J. Algebra 240 (2001), 635-664.
|
2000 |
Panyushev D., Nilpotent pairs in semisimple Lie algebras and their characteristics,
Intern. Math. Res. Notices, no. 1 (2000), 1-21.
|
1999 |
Panyushev D., Complexity and rank of actions in invariant theory,
J. Math. Sci. (New York) 95 (1999), 1925-1985.
|
Panyushev D., On spherical nilpotent orbits and beyond,
Annales Institut Fourier 49 (1999), 1453-1476.
|
Panyushev D., Vinberg E.B., An infinitesimal characterization of the complexity of homogeneous
spaces, Transformation Groups 4 (1999), 97-101.
|
Panyushev D., Parabolic subgroups with Abelian unipotent radical as a testing site
for Invariant Theory,
Can. J. Math. 51(3) (1999), 616-635.
|
Panyushev D., Actions of "nilpotent tori" on $G$-varieties,
Indagationes Math. 10(4) (1999), 565-579.
|
Panyushev D., On actions of a maximal torus on orbits of highest
weight vectors,
J. of Algebra 212 (1999), 683-702.
|
Panyushev D., On the conormal bundle of a $G$-stable subvariety,
Manuscripta Math. 99 (1999), 185-202.
|
1997 |
Panyushev D., On deformation Method in Invariant Theory,
Annales Institut Fourier 47 (1997), 985-1012.
|
Panyushev D., Cones of highest weight vectors, weight polytopes, and Lusztig’s
$q$-analog,
Transformation Groups 2 (1997), 91-115.
|
1995 |
Panyushev D., Reductive group actions on affine varieties and their doubling,
Annales Institut Fourier 45 (1995), 929–950.
|
Panyushev D., Good properties of algebras of invariants and defect of linear
representations,
Journal of Lie Theory 5 (1995), 81-99.
|
Panyushev D., On homogeneous spaces of rank one,
Indagationes Math. 6 (1995), 315-323.
|
Panyushev D., A restriction theorem and the Poincare series for $U$-invariants,
Math. Annalen 301 (1995), 655–675.
|
1994 |
Gurevich D., Panyushev D., On Poisson pairs associated to modified $R$-matrices,
Duke Math. J. 73 (1994), 249–255.
|
Panyushev D., Complexity and nilpotent orbits, Manuscripta Math.
83 (1994), 223–237.
|
Panyushev D., The Jacobian modules of a Lie algebra and geometry of commuting
varieties, Compositio Math. 94 (1994), 181-199.
|
1993 |
Panyushev D., Complexity and rank of double cones and tensor product decompositions,
Comment. Math. Helvetici 68(1993), 455-468.
|
1992 |
Panyushev D., Complexity of quasiaffine homogeneous varieties, t-decompositions and affine homogeneous
spaces of complexity 1, in: Vinberg, E.B., (Ed.) “Lie groups, their discrete
subgroups and Invariant Theory” (Adv. Sov. math., vol.8, pp.151–166) Providence:
AMS 1992.
|
Panyushev D., Affine quasihomogeneous SL(2)-varieties: Hilbert function and blow-ups, in: Vinberg,
E.B., (Ed.) “Lie groups, their discrete subgroups and Invariant Theory” (Adv. Sov.
math., vol.8, pp.131–149) Providence: AMS 1992.
|
1990 |
Panyushev D., Complexity and rank of homogeneous spaces, Geometriae Dedicata 34(1990),
249–269.
|