Corpus ID: 235458465

# New structure on the quantum alcove model with applications to representation theory and Schubert calculus

@inproceedings{Kouno2021NewSO,
title={New structure on the quantum alcove model with applications to representation theory and Schubert calculus},
author={Takafumi Kouno and C. Lenart and S. Naito},
year={2021}
}
• Published 2021
• Mathematics
The quantum alcove model associated to a dominant weight plays an important role in many branches of mathematics, such as combinatorial representation theory, the theory of Macdonald polynomials, and Schubert calculus. For a dominant weight, it is proved by Lenart-Lubovsky that the quantum alcove model does not depend on the choice of a reduced alcove path, which is a shortest path of alcoves from the fundamental one to its translation by the given dominant weight. This is established through… Expand

#### References

SHOWING 1-10 OF 21 REFERENCES
A Bijective Proof of the ASM Theorem, Part I: The Operator Formula
• Computer Science, Mathematics
• Electron. J. Comb.
• 2020
This paper provides the first bijective proof of the operator formula for monotone triangles, which has been the main tool for several non-combinatorial proofs of such equivalences. Expand
A Chevalley formula for semi-infinite flag manifolds and quantum K-theory (Extended abstract)
• Mathematics
• 2019
We give a combinatorial Chevalley formula for an arbitrary weight, in the torus-equivariant K-theory of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As anExpand
Chevalley formula for anti-dominant weights in the equivariant K-theory of semi-infinite flag manifolds
• Mathematics
• 2018
We prove a Pieri-Chevalley formula for anti-dominant weights and also a Monk formula in the torus-equivariant $K$-group of the formal power series model of semi-infinite flag manifolds, both of whichExpand
Equivariant $K$-theory of semi-infinite flag manifolds and Pieri-Chevalley formula
• Mathematics
• 2017
We propose a definition of equivariant (with respect to an Iwahori subgroup) $K$-theory of the formal power series model $\mathbf{Q}_{G}$ of semi-infinite flag manifold and prove the Pieri-ChevalleyExpand
Generalized Weyl modules and Demazure submodules of level-zero extremal weight modules.
We study a relationship between the graded characters of generalized Weyl modules $W_{w \lambda}$, $w \in W$, over the positive part of the affine Lie algebra and those of specific quotients $V_{w}^-Expand A Uniform Model for Kirillov–Reshetikhin Crystals II. Alcove Model, Path Model, and$P=X$• Mathematics • 2016 Author(s): Lenart, Cristian; Naito, Satoshi; Sagaki, Daisuke; Schilling, Anne; Shimozono, Mark | Abstract: We establish the equality of the specialization$P_\lambda(x;q,0)$of the MacdonaldExpand A UNIFORM MODEL FOR KIRILLOV–RESHETIKHIN CRYSTALS III: NONSYMMETRICMACDONALD POLYNOMIALS AT t = 0 AND DEMAZURE CHARACTERS • Mathematics • 2015 We establish the equality of the specialization Ewλ(x ; q; 0) of the nonsymmetric Macdonald polynomial Ewλ(x ; q; t) at t = 0 with the graded character gch Uw+(λ) of a certain Demazure-type submoduleExpand A uniform realization of the combinatorial$R\$-matrix
• Mathematics
• 2015
Kirillov-Reshetikhin crystals are colored directed graphs encoding the structure of certain finite-dimensional representations of affine Lie algebras. A tensor products of column shapeExpand
Generalized Weyl modules, alcove paths and Macdonald polynomials
• Mathematics
• 2015
Classical local Weyl modules for a simple Lie algebra are labeled by dominant weights. We generalize the definition to the case of arbitrary weights and study the properties of the generalizedExpand
Semi-infinite Lakshmibai-Seshadri path model for level-zero extremal weight modules over quantum affine algebras
• Mathematics
• 2014
We introduce semi-infinite Lakshmibai-Seshadri paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual BruhatExpand