D. Panyushev - Publications


Panyushev D., Nilpotent orbits and mixed gradings of semisimple Lie algebras, Indagationes Mathematicae, 32 (2021) http://iitp.ru/https://doi.org/10.1016/j.indag.2021.01.007


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


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


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


Panyushev D., Yakimova O.S., Symmetric invariants related to representations of exceptional simple groups, . . -, .78 (2017), . 2, .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


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


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


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


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


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


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


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), 315342. 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.


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.


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.


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.


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.


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.


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.


Panyushev D., Some amazing properties of spherical nilpotent orbits, Math. Zeitschrift, 245 (2003), 557580.
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.


Akhiezer D., Panyushev D., Multiplicities in the branching rules and the complexity of homogeneous spaces, Moscow Math. Journal, 2 (2002), 1733.
Panyushev D., On covariants of reductive algebraic groups, Indagationes Math. 13 (2002), 125-129.


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.


Panyushev D., Nilpotent pairs in semisimple Lie algebras and their characteristics, Intern. Math. Res. Notices, no. 1 (2000), 1-21.


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.


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.


Panyushev D., Reductive group actions on affine varieties and their doubling, Annales Institut Fourier 45 (1995), 929950.
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), 655675.


Gurevich D., Panyushev D., On Poisson pairs associated to modified $R$-matrices, Duke Math. J. 73 (1994), 249255.
Panyushev D., Complexity and nilpotent orbits, Manuscripta Math. 83 (1994), 223237.
Panyushev D., The Jacobian modules of a Lie algebra and geometry of commuting varieties, Compositio Math. 94 (1994), 181-199.


Panyushev D., Complexity and rank of double cones and tensor product decompositions, Comment. Math. Helvetici 68(1993), 455-468.


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.151166) 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.131149) Providence: AMS 1992.


Panyushev D., Complexity and rank of homogeneous spaces, Geometriae Dedicata 34(1990), 249269.