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Description: |
The right and left key maps for Kashiwara-Nakashima tableaux are used to describe type C Demazure and opposite Demazure crystals, respectively. For instance, Fu-Lascoux non-symmetric Cauchy kernels expand into products of opposite Demazure characters and Demazure atoms. These key maps are related via the Lusztig involution and it has been shown that each type C key map can be computed using the Lecouvey-Sheats symplectic jeu de taquin (Lecouvey-Jacon 2020, S. 2021). In fact, following Lascoux's ideas on type A double crystal graphs (2002), and, more recently, of Heo-Kwon (2020) and Gerber-Lecouvey (2021), we can say that a Kashiwara-Nakashima tableau T of partition shape, together with the set of minimal skew tableaux connected to it, via symplectic jeu de taquin, is endowed with a type A crystal structure, called cocrystal. Thus we have an action of the symmetric group on the column lengths of T. In particular, the skew tableaux whose column lengths are a permutation of the column lengths of T can be used to calculate the left and right key maps. On the other hand, motivated by Willis' direct way for computing type A right and left keys (2011), we also give a way of computing symplectic right and left keys without the use of jeu de taquin.
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
João Miguel Santos (PhD student, CMUC)
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Institution: |
CMUC
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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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