358 research outputs found
The Howe duality and the Projective Representations of Symmetric Groups
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 irreducible representations of a certain algebra
A_n. Recently M.~Nazarov realized irreducible representations of A_n and Young
symmetrizers by means of the Howe duality between the Lie superalgebra q(n) and
the Hecke algebra H_n, the semidirect product of S_n with the Clifford algebra
C_n on n indeterminates.
Here I construct one more analog of Young symmetrizers in H_n as well as the
analogs of Specht modules for A_n and H_n.Comment: 9 p., Late
The invariant polynomials on simple Lie superalgebras
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 induces an isomorphism between the algebra of G-invariant
polynomials on G with the algebra of W-invariant polynomals on H, where W is
the Weyl group of G, (2) each G-invariant polynomial is a linear combination of
the powers of traces tr r(x), where r is a finite dimensional representation of
G.
None of these facts is necessarily true for simple Lie superalgebras. We
reformulate Chevalley's theorem so as to embrace Lie superalgebras.
Chevalley's theorem for anti-invariant polynomials is also given.Comment: 28 p., Late
Religion and Globalization: Crossroads and Opportunities
A conversation between the First Vice-President of the Russian Philosophical Society, Doctor of Philosophy, Professor of Moscow State University, Alexander Chumakov and the editor of the special series Contemporary Russian Philosophy at Brill, the Nertherlands, Doctor of Philosophy, Professor Mikhail Sergeev
Combinatorics of irreducible characters for Lie superalgebra
In this paper we give a new formula for characters of finite dimensional
irreducible modules. We use two main ingredients: Su-Zhang
formula and Brion's theorem.Comment: 19 pages. Typos correcte
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