184 research outputs found
The flush statistic on semistandard Young tableaux
In this note, a statistic on Young tableaux is defined which encodes data
needed for the Casselman-Shalika formula.Comment: 6 page
A rigged configuration model for
We describe a combinatorial realization of the crystals and
using rigged configurations in all symmetrizable Kac-Moody types
up to certain conditions. This includes all simply-laced types and all
non-simply-laced finite and affine types
Connecting marginally large tableaux and rigged configurations via crystals
We show that the bijection from rigged configurations to tensor products of
Kirillov-Reshetikhin crystals extends to a crystal isomorphism between the
models given by rigged configurations and marginally large
tableaux.Comment: 22 pages, 3 figure
Young tableaux, canonical bases and the Gindikin-Karpelevich formula
A combinatorial description of the crystal B(infinity) for finite-dimensional
simple Lie algebras in terms of certain Young tableaux was developed by J. Hong
and H. Lee. We establish an explicit bijection between these Young tableaux and
canonical bases indexed by Lusztig's parametrization, and obtain a
combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum
over the set of Young tableaux.Comment: 19 page
Combinatorial descriptions of the crystal structure on certain PBW bases (extended abstract)
Lusztig's theory of PBW bases gives a way to realize the infinity crystal for
any simple complex Lie algebra where the underlying set consists of Kostant
partitions. In fact, there are many different such realizations, one for each
reduced expression for the longest element of the Weyl group. There is an
algorithm to calculate the actions of the crystal operators, but it can be
quite complicated. For ADE types, we give conditions on the reduced expression
which ensure that the corresponding crystal operators are given by simple
combinatorial bracketing rules. We then give at least one reduced expression
satisfying our conditions in every type except , and discuss the resulting
combinatorics. Finally, we describe the relationship with more standard
tableaux combinatorics in types A and D.Comment: Extended abstract to appear in proceedings for FPSAC 201
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