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21
Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra gl(m|n)
- J. AMS
, 2002
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A new proof of the Mullineux conjecture
- Journal of Algebraic Combinatorics
"... Let Sn be the symmetric group on n letters, k be a field of characteristic p and Dλ be the irreducible kSn-module corresponding to a p-regular partition λ of n, as in [12]. By tensoring Dλ with the 1-dimensional sign representation we obtain another irreducible kSn-module. If p = 0, Dλ ⊗ sgn ∼ = Dλ ..."
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Cited by 31 (5 self)
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Let Sn be the symmetric group on n letters, k be a field of characteristic p and Dλ be the irreducible kSn-module corresponding to a p-regular partition λ of n, as in [12]. By tensoring Dλ with the 1-dimensional sign representation we obtain another irreducible kSn-module. If p = 0, Dλ ⊗ sgn ∼ = Dλ ′ , where
REPRESENTATIONS OF LIE SUPERALGEBRAS IN PRIME CHARACTERISTIC II: THE QUEER SERIES
, 902
"... Abstract. The modular representation theory of the queer Lie superalgebra q(n) over characteristic p> 2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters χ and a criterion for the semisimplicity of the corresponding reduced enveloping al ..."
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Cited by 13 (3 self)
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Abstract. The modular representation theory of the queer Lie superalgebra q(n) over characteristic p> 2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters χ and a criterion for the semisimplicity of the corresponding reduced enveloping algebras Uχ(q(n)). A (2p)-power divisibility of dimensions of q(n)-modules with nilpotent p-characters is established. The representation theory of q(2) is treated in detail. We formulate a Morita super-equivalence conjecture for q(n) with general p-characters which is verified for n = 2. Contents
Chevalley supergroups
, 2009
"... In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. This provides a unified approach to most of the algebraic supergroups ..."
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Cited by 7 (3 self)
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In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. This provides a unified approach to most of the algebraic supergroups considered so far in literature, and an effective method to construct new ones. As an intermediate step, we prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.
JAMES ’ REGULARIZATION THEOREM FOR DOUBLE COVERS OF SYMMETRIC GROUPS
"... In [Ja1], Gordon James described leading terms in decomposition matrices and branching rules for representations of symmetric groups. To be more precise, let F be a field of characteristic p and Sn be the symmetric group. ..."
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Cited by 3 (2 self)
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In [Ja1], Gordon James described leading terms in decomposition matrices and branching rules for representations of symmetric groups. To be more precise, let F be a field of characteristic p and Sn be the symmetric group.
Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes
, 2013
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ON THE CONSTRUCTION OF CHEVALLEY SUPERGROUPS
"... We give a description of the construction of Chevalley supergroups, providing some explanatory examples. We avoid the discussion of the A(1; 1), P (3) and Q(n) cases, for which our construction holds, but the exposigetion becomes more complicated. We shall not in general provide complete proofs for ..."
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Cited by 1 (0 self)
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We give a description of the construction of Chevalley supergroups, providing some explanatory examples. We avoid the discussion of the A(1; 1), P (3) and Q(n) cases, for which our construction holds, but the exposigetion becomes more complicated. We shall not in general provide complete proofs for our statements, instead we will make an effort to convey the key ideas underlying our construction. A fully detailed account of our work is scheduled to appear in [9]. 1
doi:10.1093/imrn/rnt262 Presenting Queer Schur Superalgebras
"... Associated to the two types of finite-dimensional simple superalgebras, there are the general linear Lie superalgebra and the queer Lie superalgebra. The universal envelop-ing algebras of these Lie superalgebras act on the tensor spaces of the natural represen-tations and, thus, define certain finit ..."
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Associated to the two types of finite-dimensional simple superalgebras, there are the general linear Lie superalgebra and the queer Lie superalgebra. The universal envelop-ing algebras of these Lie superalgebras act on the tensor spaces of the natural represen-tations and, thus, define certain finite-dimensional quotients, the Schur superalgebras, and the queer Schur superalgebra. In this paper, we introduce the quantum analog of the queer Schur superalgebra and investigate the presentation problem for both the queer Schur superalgebra and its quantum analog. 1
