Results 11 to 20 of about 119 (86)

Towards plethystic \(\mathfrak{sl}_2\) crystals

Combinatorial Theory
To find crystals of \(\mathfrak{sl}_2\) representations of the form \(\Lambda^n\operatorname{Sym}^r\mathbb{C}^2\) it suffices to solve the combinatorial problem of decomposing the Young lattice into symmetric, saturated chains.
Álvaro Gutiérrez
semanticscholar   +2 more sources

Positively multiplicative graphs and homology rings of affine Grassmannians

Combinatorial Theory
Let \(\mathfrak{g}\) be an untwisted affine Lie algebra with associated Weyl group \(W_a\) and let \(W\) be the Weyl group of the corresponding simple Lie algebra.
Jérémie Guilhot, Cédric Lecouvey, Pierre Tarrago   +2 more
semanticscholar   +2 more sources

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
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
core   +1 more source

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
core   +1 more source

Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
This is the first of three papers that develop structures which are counted by a "parabolic" generalization of Catalan numbers. Fix a subset R of {1,..,n-1}. Consider the ordered partitions of {1,..,n} whose block sizes are determined by R. These are the
Robert A. Proctor, Matthew J. Willis
doaj   +1 more source

Littlewood–Richardson coefficients via mirror symmetry for cluster varieties

Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 463-512, September 2020., 2020
Abstract I prove that the full Fock–Goncharov conjecture holds for Conf3×(Fℓ∼) — the configuration space of triples of decorated flags in generic position. As a key ingredient of this proof, I exhibit a maximal green sequence for the quiver of the initial seed.
Timothy Magee
wiley   +1 more source

SCHUR-WEYL DUALITIES FOR SYMMETRIC INVERSE SEMIGROUPS [PDF]

, 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, Mazorchuk, Volodymyr,, Volodymyr Mazorchuk, Ganna Kudryavtseva   +4 more
core   +1 more source

Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials) [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Robert A. Proctor, Matthew J. Willis
doaj   +1 more source