کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425427 1633803 2015 40 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Hall-Littlewood polynomials and characters of affine Lie algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Hall-Littlewood polynomials and characters of affine Lie algebras
چکیده انگلیسی

The Weyl-Kac character formula gives a beautiful closed-form expression for the characters of integrable highest-weight modules of Kac-Moody algebras. It is not, however, a formula that is combinatorial in nature, obscuring positivity. In this paper we show that the theory of Hall-Littlewood polynomials may be employed to prove Littlewood-type combinatorial formulas for the characters of certain highest weight modules of the affine Lie algebras Cn(1), A2n(2) and Dn+1(2). Through specialisation this yields generalisations for Bn(1), Cn(1), A2n−1(2), A2n(2) and Dn+1(2) of Macdonald's identities for powers of the Dedekind eta-function. These generalised eta-function identities include the Rogers-Ramanujan, Andrews-Gordon and Göllnitz-Gordon q-series as special, low-rank cases.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 285, 5 November 2015, Pages 1066-1105
نویسندگان
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