Cactus group actions on shifted tableau crystals and a shifted Berenstein-Kirillov group
 
 
Description:  Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure for shifted tableaux, called the shifted tableau crystal. We introduce a shifted version of the crystal reflection operators, which coincide with the restrictions of the shifted Schützenberger involution to any primed interval of two adjacent letters. Unlike type A Young tableau crystals, these operators do not realize an action of the symmetric group on the shifted tableau crystal since the braid relations do not need to hold. Following a similar approach as Halacheva, we exhibit a natural internal action of the cactus group on this crystal, realized by the restrictions of the shifted Schützenberger involution to all primed intervals of the underlying crystal alphabet, containing, in particular, the aforesaid action of the shiftedcrystal reflection operators analogues.

In addition, we exhibit another occurrence of a cactus group action on shifted tableau crystals, that differs from the previous one on skew shapes and coincides on straight shapes. We use the shifted tableau switching introduced by Choi, Nam and Oh to define a shifted version of the Bender-Knuth operators on shifted semistandard tableaux. Following the work of Chmutov, Glick and Pylyavskyy, we use these operators on straight shapes to provide a shifted analogue of the Berenstein-Kirillov group and show that it is isomorphic to a quotient of the cactus group.

Date:  2020-07-01
Start Time:   14:30
Speaker:  Inês Rodrigues (CEAFEL, Univ. Lisboa)
Institution:  CEAFEL, Univ. Lisboa
Place:  Zoom: https://videoconf-colibri.zoom.us/j/95183287899?pwd=VnNXRjkrRlkybzJZNU1ISE91Q2c1QT09
Research Groups: -Algebra and Combinatorics
See more:   <Main>  
 
© Centre for Mathematics, University of Coimbra, funded by
Science and Technology Foundation
Powered by: rdOnWeb v1.4 | technical support