Corpus ID: 237571679

On Sch\"utzenberger modules of the cactus group

@inproceedings{Lim2021OnSM,
  title={On Sch\"utzenberger modules of the cactus group},
  author={Jongmin Lim and Oded Yacobi},
  year={2021}
}
  • Jongmin Lim, Oded Yacobi
  • Published 20 September 2021
  • Mathematics
The cactus group acts on the set of standard Young tableau of a given shape by (partial) Schützenberger involutions. It is natural to extend this action to the corresponding Specht module by identifying standard Young tableau with the Kazhdan-Lusztig basis. We term these representations of the cactus group “Schützenberger modules”, denoted S Sch, and in this paper we investigate their decomposition into irreducible components. We prove that when λ is a hook shape, the cactus group action on S… Expand

References

SHOWING 1-10 OF 16 REFERENCES
The Berenstein–Kirillov group and cactus groups
Berenstein and Kirillov have studied the action of Bender-Knuth moves on semistandard tableaux. Losev has studied a cactus group action in Kazhdan-Lusztig theory; in type $A$ this action can also beExpand
Representations of Coxeter groups and Hecke algebras
here l(w) is the length of w. In the case where Wis a Weyl group and q is specialized to a fixed prime power, | ~ can be interpreted as the algebra of intertwining operators of the space of functionsExpand
GROUPS GENERATED BY INVOLUTIONS GELFAND TSETLIN PATTERNS AND COMBINATORICS OF YOUNG TABLEAUX
We construct families of piecewise linear representations cpl representations of the symmetric group Sn and the a ne Weyl group e Sn of type A n acting on the space of triangles Xn We nd a nontrivialExpand
Relations between Young's natural and the Kazhdan-Lusztig representations of Sn
Abstract Our main result here is that, under a suitable order of standard tableaux, the classical representation of Sn introduced by Young (in “The Collected Papers of Alfred Young, 1873–1940,” Univ.Expand
Cacti and cells
  • I. Losev
  • Mathematics
  • Journal of the European Mathematical Society
  • 2019
The goal of this paper is to construct an action of the cactus group of a Weyl group W on W that is nicely compatible with Kazhdan-Lusztig cells. The action is realized by the wall-crossingExpand
Fundamental Groups of Blow-ups
Abstract Many examples of nonpositively curved closed manifolds arise as real blow-ups of projective hyperplane arrangements. If the hyperplane arrangement is associated to a finite reflection groupExpand
Crystals and coboundary categories
Following an idea of A. Berenstein, we define a commutor for the category of crystals of a finite dimensional complex reductive Lie algebra. We show that this endows the category of crystals with theExpand
Crystals and monodromy of Bethe vectors
Fix a semisimple Lie algebra g. Gaudin algebras are commutative algebras acting on tensor product multiplicity spaces for g-representations. These algebras depend on a parameter which is a point inExpand
Cyclic sieving, promotion, and representation theory
  • B. Rhoades
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2010
TLDR
Kazhdan-Lusztig theory is used and a characterization of the dual canonical basis of C[x"1"1,...,x"n"n] due to Skandera is characterized, suggesting a possible sieving phenomenon for dihedral groups. Expand
Introduction to Quantum Groups and Crystal Bases
Lie algebras and Hopf algebras Kac-Moody algebras Quantum groups Crystal bases Existence and uniqueness of crystal bases Global bases Young tableaux and crystals Crystal graphs for classical LieExpand
...
1
2
...