منابع مشابه
Schur functions and a ne Lie algebras
We make use of the representation theory of the innnite dimensional Lie algebras a 1 , b 1 and b sl 2 to derive explicit formulas relating Schur's P-functions to Schur's S-functions. R esum e Nous utilisons la th eorie des repr esentations des alg ebres de Lie de dimension innnie a 1 , b 1 et b sl 2 pour obtenir des formules explicites reliant les fonctions P de Schur aux fonctions S de Schur.
متن کاملGeneral branching functions of affine Lie algebras
Explicit expressions are presented for general branching functions for cosets of affine Lie algebras ĝ with respect to subalgebras ĝ′ for the cases where the corresponding finite dimensional algebras g and g′ are such that g is simple and g′ is either simple or sums of u(1) terms. A special case of the latter yields the string functions. Our derivation is purely algebraical and has its origin i...
متن کاملRectangular Schur functions and the basic representation of affine Lie algebras
An expression is given for the plethysm p2 ◦ S , where p2 is the power sum of degree two and S is the Schur function indexed by a rectangular partition. The formula can be well understood from the viewpoint of the basic representation of the affine Lie algebra of type A (2) 2
متن کاملPresenting affine q-Schur algebras
We obtain a presentation of certain affine q-Schur algebras in terms of generators and relations. The presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine gln. Our results extend and rely on the corresponding result for the q-Schur algebra of the symmetric group, which were proved by the first author and Giaquinto. Mathem...
متن کاملSymplectic Reflection Algebras and Affine Lie Algebras
These are the notes of my talk at the conference “Double affine Hecke algebras and algebraic geometry” (MIT, May 18, 2010). The goal of this talk is to discuss some results and conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the representation theory for affine Lie algebras. These conjectures arose fr...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7453