Matrix-Ball Construction of affine Robinson–Schensted correspondence

  title={Matrix-Ball Construction of affine Robinson–Schensted correspondence},
  author={Michael Chmutov and Pavlo Pylyavskyy and Elena Yudovina},
  journal={Selecta Mathematica},
In his study of Kazhdan–Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson–Schensted correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to give a more combinatorial realization of Shi’s algorithm. As a byproduct, we also give a way to realize the affine correspondence via the usual Robinson–Schensted bumping algorithm. Next, inspired by Lusztig and Xi, we extend the algorithm to a bijection between the extended affine symmetric group… 

Sign insertion and Kazhdan-Lusztig cells of affine symmetric groups.

Combinatorics of Kazhdan-Lusztig cells in affine type $A$ was originally developed by Lusztig, Shi, and Xi. Building on their work, Chmutov, Pylyavskyy, and Yudovina introduced the affine matrix-ball

Affine RSK correspondence and crystals of level zero extremal weight modules

We give an affine analogue of the Robison-Schensted-Knuth (RSK) correspondence, which generalizes the affine Robinson-Schensted correspondence by ChmutovPylyavskyy-Yudovina. The affine RSK map sends

Affine Springer Fibers and the Affine Matrix Ball Construction for Rectangular Type Nilpotents

In this paper, we study the affine Springer fiber $\mathcal{F} l_N$ in type $A$ for rectangular type semisimple nil-element $N$ and calculate the relative position between irreducible components. In

Monodromy in Kazhdan–Lusztig cells in affine type A

We use the affine Robinson-Schensted correspondence to describe the structure of bidirected edges in the Kazhdan-Lusztig cells in affine type A. Equivalently, we give a comprehensive description of

Poset associahedra

For each poset P , we construct a polytope A (P ) called the P -associahedron. Similarly to the case of graph associahedra, the faces of A (P ) correspond to certain tubings of P . The Stasheff

Kazhdan--Lusztig cells of $\mathbf{a}$-value 2 in $\mathbf{a}(2)$-finite Coxeter systems

A Coxeter group is said to be a(2)-finite if it has finitely many elements of a-value 2 in the sense of Lusztig. In this paper, we give explicit combinatorial descriptions of the left, right, and

Two-row W-graphs in affine type A

Affine symmetric group

The affine symmetric group is a mathematical structure that describes the symmetries of the number line and the regular triangular tesselation of the plane, as well as related higher dimensional

Cyclic quasi-symmetric functions

The ring of cyclic quasi-symmetric functions and its non-Escher subring are introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; for the non-Escher



The Kazhdan-Lusztig cells in certain affine Weyl groups

Coxeter groups, Hecke algebras and their representations.- Applications of Kazhdan-Lusztig theory.- Geometric interpretations of the Kazhdan-Lusztig polynomials.- The algebraic descriptions of the

Cells in affine Weyl groups, II

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 functions

Robinson-Schensted correspondence and left cells

Although the Robinson-Schensted-Knuth correspondence is a classical subject, its study is still active because of new development in last two decades. In this field, fundamental results are sometimes

The Structure of Sperner k-Families

The based ring of two-sided cells of affine Weyl groups of type ̃_{-1}

  • N. Xi
  • Mathematics, Biology
  • 2002
Cells in affine Weyl groups Type $\widetilde{A}_{n-1}$ Canonical left cells The group $F_\lambda$ and its representation A bijection between $\Gamma_\lambda\cap\Gamma^{-1}_\lambda$ and Irr


We introduce a group of periodic permutations, a new version of the infinite symmetric group. We then generalize and study the Robinson–Schensted correspondence for such permutations.