# SHIFTED TABLEAU SWITCHINGS AND SHIFTED LITTLEWOOD-RICHARDSON COEFFICIENTS

Choi, Seung-Il;Nam, Sun-Young;Oh, Young-Tak

• Accepted : 2018.11.29
• Published : 2019.07.01
• 46 5

#### Abstract

We provide two shifted analogues of the tableau switching process due to Benkart, Sottile, and Stroomer; the shifted tableau switching process and the modified shifted tableau switching process. They are performed by applying a sequence of elementary transformations called switches and shares many nice properties with the tableau switching process. For instance, the maps induced from these algorithms are involutive and behave very nicely with respect to the lattice property. We also introduce shifted generalized evacuation which exactly agrees with the shifted J-operation due to Worley when applied to shifted Young tableaux of normal shape. Finally, as an application, we give combinatorial interpretations of Schur P- and Schur Q-function related identities.

#### Keywords

shifted tableau switchings;shifted jeu de taquin;Schur P- and Schur Q-functions;shifted Littlewood-Richardson coefficients

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#### Acknowledgement

Supported by : NRF, Samsung Science and Technology Foundation