# Matrix-Ball Construction of affine Robinson–Schensted correspondence

@article{Chmutov2020MatrixBallCO, title={Matrix-Ball Construction of affine Robinson–Schensted correspondence}, author={Michael Chmutov and Pavlo Pylyavskyy and Elena Yudovina}, journal={Selecta Mathematica}, year={2020}, volume={24}, pages={667-750} }

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…

## 15 Citations

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

- Mathematics
- 2020

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

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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

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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…

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- 2022

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…

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- 2021

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…

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### Affine symmetric group

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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

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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…

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