Results 11 to 20 of about 74 (74)

Crystal structures on FFLV polytopes [PDF]

, 2021
In this paper we formulate a conjecture about the crystal structures on Feigin--Fourier--Littelmann--Vinberg (FFLV) polytopes and prove it in small rank examples.
Fang, Xin, Koshevoy, Gleb, Gleb Koshevoy, Xin Fang, Fang, Xin ; Koshevoy, Gleb   +4 more
core   +1 more source

A horizontal-strip LLT polynomial is determined by its weighted graph [PDF]

, 2023
We prove that two horizontal-strip LLT polynomials are equal if the associated weighted graphs defined by the author in a previous paper are isomorphic.
Tom, Foster
core   +1 more source

A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials [PDF]

, 2021
In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of the horizontal-strip LLT polynomial \(G_{\boldsymbol\lambda}(\boldsymbol x;q)\) in some special cases. We associate a weighted graph \(\Pi\) to \(\
Tom, Foster, Foster Tom
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A combinatorial basis for the fermionic diagonal coinvariant ring [PDF]

, 2023
Let \(\Theta_n = (\theta_1, \dots, \theta_n)\) and \(\Xi_n = (\xi_1, \dots, \xi_n)\) be two lists of \(n\) variables and consider the diagonal action of \(\mathfrak{S}_n\) on the exterior algebra \(\wedge \{ \Theta_n, \Xi_n \}\) generated by these ...
Kim, Jesse, Jesse Kim
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Increasing subsequences, matrix loci and Viennot shadows

Forum of Mathematics, Sigma
Let ${\mathbf {x}}_{n \times n}$ be an $n \times n$ matrix of variables, and let ${\mathbb {F}}[{\mathbf {x}}_{n \times n}]$ be the polynomial ring in these variables over a field ${\mathbb {F}}$ .
Brendon Rhoades
doaj   +1 more source

SCHUR-WEYL DUALITIES FOR SYMMETRIC INVERSE SEMIGROUPS

, 2008
. We obtain Schur-Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations.
Kudryavtseva, Ganna, Mazorchuk, Volodymyr,, Volodymyr Mazorchuk, Ganna Kudryavtseva   +3 more
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DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY

Forum of Mathematics, Sigma, 2015
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive.
SAMI H. ASSAF
doaj   +1 more source

Branching rules of minuscule representations via a new partial order [PDF]

We introduce a new partial order on the set of all antichains of a fixed size in any poset. When applied to minuscule posets, these partial orders give rise to distributive lattices that appear in the branching rules for minuscule representations of ...
Green, R. M., Xu, Tianyuan
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Δ–Springer varieties and Hall–Littlewood polynomials

Forum of Mathematics, Sigma
The $\Delta $ -Springer varieties are a generalization of Springer fibers introduced by Levinson, Woo and the author that have connections to the Delta Conjecture from algebraic combinatorics.
Sean T. Griffin
doaj   +1 more source

Baby Verma modules for rational Cherednik algebras

, 2003
This paper introduces baby Verma modules for symplectic reflection algebras of complex reflection groups at parameter t = 0 (the so-called rational Cherednik algebras at parameter t = 0, and presents their most basic properties.
Gordon, I.
core   +1 more source