The symplectic left companion of a Littlewood-Richardson-Sundaram tableau and the Kwon condition

As a consequence of the Littlewood-Richardson  commuters coincidence and the Kumar-Torres branching model  via  Kushwaha-Raghavan-Viswanath flagged hives, we have solved the Lecouvey-Lenart conjecture on the  bijections between the Kwon and Sundaram branching models for  the pair (GL_2n(C), Sp_2n(C)) consisting of the general linear group GL_2n(C) and  the symplectic group Sp_2n(C). In particular, thanks to the Henriques-Kamnitzer gl_n-crystal commuter, we have    recognized that the left companion of a Littlewood-Richardson-Sundaram tableau is characterized by the   Kwon  symplectic condition. We now show that a Littlewood-Richardson-Sundaram tableau naturally mirrors, by construction, on its left companion the  symplectic Kwon condition.

--------------------------------------------------------------------------------

There will be coffee and cake after the seminar in the common room