Shifted tableau switchings and shifted Littlewood--Richardson coefficients
J. Korean Math. Soc. 2019 Vol. 56, No. 4, 947-984
https://doi.org/10.4134/JKMS.j180488
Published online July 1, 2019
Seung-Il Choi, Sun-Young Nam, Young-Tak Oh
Seoul National University; Sogang University; Sogang University
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 {\it 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
MSC numbers : 05E05
Supported by : The first author was supported by NRF Grant #2012R1A1A2001635, NRF Grant #2015R1D1-A1A01056670 and Samsung Science and Technology Foundation under Project Number SSTF-BA1501-01. The second author was supported by NRF Grant #2012R1A1A2001635, NRF Grant #2015R1D1-A1A01056670 and NRF Grant #2017R1D1A1B03030945. The third author was supported by NRF Grant #2012R1A1A2001635 and NRF Grant #2015R1D1-A1A01056670
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