Kostka-Shoji Polynomials and Lusztig's Convolution Diagram
نویسندگان
چکیده
منابع مشابه
Paths 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 کاملThe 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 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 کاملRIMS - 1654 Paths 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 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: Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES
سال: 2018
ISSN: 2304-7895,2304-7909
DOI: 10.21915/bimas.2018102