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Selected Publications of Dmitri Panyushev
Complexity and rank of double cones and tensor product decompositions,
Comment. Math. Helvetici 68(1993), 455-468.
The Jacobian modules of a Lie algebra and geometry of commuting
varieties, Compositio Math. 94 (1994), 181-199.
Complexity and nilpotent orbits, Manuscripta Math.
83 (1994), 223-237.
(with D. Gurevich)
On Poisson pairs associated to modified $R$-matrices,
Duke Math. J. 73 (1994), 249-255.
Multiplicities of weights of some representations and convex polytopes,
Funct. Anal. Appl. 28 (1994), 293-295.
A restriction theorem and the Poincare series for $U$-invariants,
Math. Annalen 301 (1995), 655-675.
On homogeneous spaces of rank one,
Indag. Math. 6 (1995), 315-323.
Good properties of algebras of invariants and defect of linear
representations,
Journal of Lie Theory 5 (1995), 81-99.
Reductive group actions on affine varieties and their doubling,
Annales l'Institut Fourier 45 (1995), 929-950.
On double cones and tensor product decompositions,
Uspekhi matem. Nauk 51 no. 2 (1996), 171-172 (Russian).
Cones of highest weight vectors, weight polytopes, and Lusztig's
$q$-analog,
Transformation Groups 2 (1997), 91-115.
On deformation Method in Invariant Theory,
Ann. l'Institut Fourier 47 (1997), 985-1012.
On the conormal bundle of a G-stable subvariety,
Manuscripta Math. 99 (1999), 185-202.
On actions of a maximal torus on orbits of highest
weight vectors,
J. Algebra 212 (1999), 683-702.
Actions of "nilpotent tori" on $G$-varieties,
Indagationes Math. 10(4) (1999), 565-579.
Parabolic subgroups with Abelian unipotent radical as a testing site
for Invariant Theory,
Can. J. Math. 51(3) (1999), 616-635.
(with E.B. Vinberg)
An infinitesimal characterization of the complexity of homogeneous
spaces, Transformation Groups 4 (1999), 97-101.
On spherical nilpotent orbits and beyond,
Ann. Inst. Fourier 49 (1999), 1453-1476.
Complexity and rank of actions in invariant theory,
J. Math. Sci (New York) 95 (1999), 1925-1985.
Nilpotent pairs in semisimple Lie algebras and their characteristics,
Intern. Math. Res. Notices, no. 1 (2000), 1-21.
Nilpotent pairs, dual pairs, and sheets,
J. Algebra 240 (2001), 635-664.
(with A.G. Elashvili)
A classification of the principal nilpotent pairs in simple Lie
algebras and related problems,
J. London Math. Soc. 63 (2001), 299-318.
The exterior algebra and `Spin' of an orthogonal $\frak g$-module,
Transformation Groups 6 (2001), 371-396
gzipped PS.
Isotropy representations, eigenvalues of a
Casimir element, and commutative Lie subalgebras,
J. London Math. Soc. 64 (2001), 61-80.
gzipped PS.
(with G. Röhrle)
Spherical orbits and abelian ideals,
Adv. in Math. 159 (2001), 229-246.
PDF(Jour.).
Inductive formulas for the index of seaweed Lie algebras,
Moscow Math. J. 1 (2001), 221-241.
gzipped PS.
(with D.N. Akhiezer)
Multiplicities in the branching rules and
the complexity of homogeneous spaces,
Moscow Math. J. 2 (2002), 17-33.
gzipped PS.
On covariants of reductive algebraic groups,
Indagationes Math. 13 (2002), 125-129.
PDF(Jour.)
The index of a Lie algebra, the centraliser of a
nilpotent element, and the normaliser of the centraliser,
Math. Proc. Camb. Phil. Soc. 134 (2003), 41-59.
gzipped PS.
Abelian ideals of a Borel subalgebra and long positive roots,
Intern. Math. Res. Notices, no. 35 (2003), 1889-1913.
PDF(Jour.)
Some amazing properties of spherical nilpotent orbits,
Math. Zeitschrift, 245 (2003), 557-580.
PDF
On the irreducibility of commuting varieties associated with
involutions of simple Lie algebras, Funkt. Analiz i ego prilozh.38 , no.1 (2004), 47-55 (in Russian).
gzipped PS.
AD-nilpotent ideals of a Borel subalgebra: generators and duality,
J. Algebra274 (2004), 822-846 (math.RT/0303107).
Short antichains in root systems, semi-Catalan arrangements,
and B-stable subspaces, Europ. J. Combinatorics25 (2004), 93-112. PDF(Jour.)
Regions in the dominant chamber and nilpotent orbits,
Bull. Sci. Math.128 (2004), 1-6. PDF(Jour.)
Weight multiplicity free representations, $\frak g$-endomorphism algebras,
and Dynkin polynomials, J. London Math. Soc.
69, Part 2 (2004), 273-290.
PDF(Jour.)
Long Abelian ideals,
Adv. Math.186 (2004), 307-316.
On reachable elements and the boundary of nilpotent orbits in simple
Lie algebras, Bull. Sci. Math.128 (2004), 859-870.
On Invariant Theory of θ-groups,
J. Algebra283 (2005), 655-670.
(with G.Röhrle)
On spherical ideals of Borel subalgebras,
Archiv der Math.84 (2005), 225-232.
An extension of Rais' theorem
and seaweed subalgebras of simple Lie algebras,
Ann. Inst. Fourier55 (2005), no. 3, 693-715.
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
(math.RT/0311347).
Normalizers of ad-nilpotent ideals,
Europ. J. Combinatorics27 (2006), 153-178.
The poset of positive roots and its relatives,
J. Alg. Combinatorics23 (2006), 79-101
(math.CO/0502385).
(with O.Yakimova)
The index of representations associated with stabilisers,
J. Algebra, 302 (2006), 280-304.
Commutative subalgebras and sphericity in Z2-graded
Lie algebras,
Bull. London Math. Soc., 38, Part 5 (2006), 753-763.
Semi-direct products of Lie algebras, their invariants and
representations, Publ. R.I.M.S., 43, no.4 (2007),
1199-1257
(math.AG/0506579).
On the coadjoint representation of Z2-contractions of
reductive Lie algebras, Adv. Math., 213 (2007), 380-404
(math.RT/0610493).
(with A.Premet and O.Yakimova)
On symmetric invariants of centralisers in reductive Lie algebras,
J. Algebra, 313 (2007), 343-391
(math.RT/0610049).
(with O.Yakimova)
Symmetric pairs and associated commuting varieties,
Math. Proc. Cambr. Phil. Soc. 143 (2007), 307-321
(math.AG/0601534).
Two results on centralisers of nilpotent elements,
J. Pure Applied Algebra 212 (2008), 774-779.
(with O.Yakimova)
The argument shift method and maximal commutative subalgebras of
Poisson algebras,
Math. Res. Letters, 15 (2008), 239-249.
(with O.Yakimova)
The PRV-formula for tensor product decompositions and its applications,
Funct. Anal. Appl., 42, no.1 (2008), 45-52.
Adjoint vector fields and differential operators on representation
spaces, Bull. London Math. Soc., 40, no.6 (2008), 1045-1064
(arXiv:
0808.2120).
On orbits of antichains of positive roots, Europ. J.
Combinatorics, 30, no.2 (2009), 586-594.
Periodic automorphisms of Takiff algebras, contractions, and
θ-groups, Transformation Groups, 14, no.2 (2009),
463-482
(arXiv:
0710.2113).
On the Dynkin index of a principal sl(2)-subalgebra,
Adv. Math., 221, no.4 (2009), 1115-1121
(arXiv:
0903.0398).
Properties of weight posets for weight multiplicity free
representations, Moscow Math. J., 9, no. 4 (2009),
867--883
(arXiv:
0810.2919).
Actions of the derived group of a maximal unipotent subgroup on
G-varieties, IMRN, 2010 (2010), no. 4, 674-700
(arXiv:
0812.1343).
Generalised Kostka-Foulkes polynomials and cohomology of line
bundles on homogeneous vector bundles, Selecta Math., 16
(2010), 315-342
(arXiv: 0904.3721).
On divisible weighted Dynkin diagrams and reachable elements,
Transformation Groups, 15 (2010), 983-999
arXiv: 1002.4854.
(with E.B. Vinberg) The work of Vladimir Morozov on Lie algebras,
Transformation Groups, 15 (2010), 1001-1013.
Fredman's reciprocity, invariants of abelian groups, and the
permanent of the Cayley table, J. Algebraic Combin., 33 (2011),
111-125
PDF (Journ.).
Abelian ideals of a Borel subalgebra and
subsets of the Dynkin diagram, J. Algebra, 344 (2011),
197-204
(arXiv: 1008.1850).
Invariants of a maximal unipotent subgroup and equidimensionality,
Bull. Sci. Math.,136 (2012), 149-161 (Preprint series of
CRC 701 University of Bielefeld, Preprint
11110).
Invariant theory of little adjoint modules, J. Lie Theory,
22 (2012), 803-816
(arXiv: 1205.5200).
Quotients by actions of the derived group of a maximal unipotent
subgroup, Pacific J. Math., 256 (2012), 381-405
(arXiv: 1009.4051).
Two covering polynomials of a finite poset, with applications to
root systems and ad-nilpotent ideals, J. Combinatorics, 3
(2012), 63-89
(math.CO/0502386).
(with O.Yakimova)
On a remarkable contraction of semisimple Lie
algebras, Ann. Inst. Fourier, 62, no.6 (2012),
2053-2068 (arXiv:
1107.0702).
Commuting involutions and degenerations of isotropy representations,
Transformation Groups, 18, no.2 (2013),
507-537
(arXiv:
1104.5472).
Commuting involutions of Lie algebras, commuting varieties, and
simple Jordan algebras, Algebra & Number Theory, 7, no.6
(2013), 1505-1534
(arXiv:
1210.3785).
(with O.Yakimova)
Parabolic contractions of semisimple Lie algebras
and their invariants, Selecta Math., 19 (2013), 699-717
(arXiv: [math.AG]
1301.0249).
Wide subalgebras of semisimple Lie algebras, Algebras and Repr.
Theory, 17, no.3 (2014), 931-944
(arXiv: [math.RT]
1301.0488).
Abeian ideals of a Borel subalgebra and root systems,
J. Europ. Math. Soc., 16 (2014), 2693-2708
(arXiv:
1205.5983).
(with O.Yakimova)
On maximal commutative subalgebras of Poisson algebras associated with
involutions of semisimple
Lie algebras, Bull. Sci. Math., 138 (2014), 705-720
(arXiv: 1312.1872).
The Dynkin index and sl(2)-subalgebras of simple Lie algebras,
J. Algebra, 430 (2015), 15-25
(arXiv: 1311.3170).
Antichains in weight posets associated with gradings of simple
Lie algebras, Math. Z., 281 (2015), 1191-1214
(arXiv: 1411.7683).
Minimal inversion complete sets and maximal abelian ideals,
J. Algebra, 445 (2016), 163-180
(arXiv:
1505.00653).
Normalisers of abelian ideals of Borel subalgebras and Z-gradings of
a simple Lie algebra, J. Lie Theory, 26 (2016), 659-672.
(arXiv:
1512.08092).