Demazure crystals of generalized Verma modules and a flagged RSK correspondence - Mathematics > Representation Theory

Abstract: We prove that the Robinson-Schensted-Knuth correspondence is a$\gl {\infty}$-crystal isomorphism between two realizations of the crystalgraph of a generalized Verma module with respect to a maximal parabolicsubalgebra of $\gl {\infty}$. %This extends the previously known result that%the RSK correspondence is an isomorphism of bicrystals or double %crystals. Aflagged version of the RSK correspondence is derived in a natural way bycomputing a Demazure crystal graph of a generalized Verma module. As anapplication, we discuss a relation between a Demazure crystal and planepartitions with a bounded condition.

Author: Jae-Hoon Kwon

Source: https://arxiv.org/