358 research outputs found

    The Howe duality and the Projective Representations of Symmetric Groups

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    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

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    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

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    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 gl(m,n)\frak{gl}(m,n)

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    In this paper we give a new formula for characters of finite dimensional irreducible gl(m,n)\frak{gl}(m,n) modules. We use two main ingredients: Su-Zhang formula and Brion's theorem.Comment: 19 pages. Typos correcte
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