5 citations · 7 across the 3 of their papers we have counts for
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The Howe duality and the Projective Representations of Symmetric Groups
Alexander Sergeev
The symmetric group S_n possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of S_n itself, coincide with the…
An analog of the classical invariant theory for Lie superlagebras
Alexander Sergeev
Let V be a finite-dimensional superspace and G a simple (or a ``close'' to simple) matrix Lie superalgebra, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theo…
The invariant polynomials on simple Lie superalgebras
Alexander Sergeev
Chevalley's theorem states that for any simple finite dimensional Lie algebra G (1) the restriction homomorphism of the algebra of polynomials on G onto the Cartan subalgebra H ind…
Orthogonal polynomials and Lie superalgebras
Alexander Sergeev
For the orthogonal Lie algebra O(2n+1), in addition to the conventional set of orthogonal polynomials, another set is produced with the help of the Lie superalgebra OSP(1|2n). Diff…
Irreducible representations of solvable Lie superalgebras
Alexander Sergeev
The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these…