The Bailey Lemma and Kostka Polynomials
نویسندگان
چکیده
منابع مشابه
The Bailey Lemma and Kostka Polynomials
Using the theory of Kostka polynomials, we prove an An−1 version of Bailey’s lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible characters of A n−1 and to identities for A-type branching functions.
متن کاملA Higher-level Bailey Lemma
We propose a generalization of Bailey’s lemma, useful for proving q-series identities. As an application, generalizations of Euler’s identity, the Rogers–Ramanujan identities, and the Andrews–Gordon identities are derived. The generalized Bailey lemma also allows one to derive the branching functions of higher-level A (1) 1 cosets. 1. The Bailey Lemma In his famous 1949 paper, W. N. Bailey note...
متن کاملPaths and Kostka–macdonald Polynomials
We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight multiplicities of the tensor product of the fundamental representations of the Lie algebra gl(n). As an application, we give an elementary proof of the special case t = 1 of the Haglund–Haiman–Loehr formula. Also, we pr...
متن کاملUbiquity of Kostka Polynomials
We report about results revolving around Kostka–Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears that the set of all parabolic Kostka polynomials forms a semigroup, which we call Liskova semigroup. We show that polynomials frequently appearing in Representation Theory and Combinatorics belong to the Liskova semigroup. Among ...
متن کاملGeneralized Energy Statistics and Kostka–Macdonald Polynomials
We give an interpretation of the t = 1 specialization of the modified Macdonald polynomial as a generating function of the energy statistics defined on the set of paths arising in the context of Box-Ball Systems (BBS-paths for short). We also introduce one parameter generalizations of the energy statistics on the set of BBS-paths which all, conjecturally, have the same distribution. Résumé. Nou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2004
ISSN: 0925-9899
DOI: 10.1023/b:jaco.0000047280.16877.1f