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Description: |
The Bender-Knuth moves on Young tableaux are well-known involutions, namely, they are used in a combinatorial proof that the Schur functions are symmetric, as well as in alternative proofs of the classic Littlewood-Richardson rule. The group generated by these involutions, modulo the relations they satisfy on semistandard Young tableaux, is known as the Berenstein-Kirillov group, and it is isomorphic to a quotient of the cactus group. The Bender-Knuth involutions coincide with the tableau switching on horizontal border strips filled with two adjacent letters. Using the shifted tableau switching of Choi, Nam, and Oh (2019), we introduce a shifted version of the Bender-Knuth involutions, which also show that Schur Q- and P-functions are symmetric, and define a shifted Berenstein-Kirillov group. This group acts on the straight-shaped shifted tableau crystals introduced by Gillespie, Levinson and Purbhoo (2017), via the partial Schützenberger involutions, thus coinciding with a cactus group action due to the author. We will also provide alternative formulations using the type C infusion of Thomas and Yong (2009) together with the shifted semistandardization process due to Pechenik and Yong (2017). Following the works of Halacheva (2016, 2020), and Chmutov, Glick and Pylyavskyy (2017), we show that the shifted Berenstein-Kirillov group is isomorphic to a quotient of the cactus group, while providing an alternative presentation for the cactus group in terms of shifted Bender-Knuth involutions.
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
Inês Rodrigues (CEAFEL, Univ. Lisboa)
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Institution: |
CEAFEL, Univ. Lisboa
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Place: |
Zoom: https://videoconf-colibri.zoom.us/j/81787306524
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| Research Groups: |
-Algebra and Combinatorics
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See more:
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