arXiv subjects
Publications and source records attributed to K. C. Misra.
We study, in the path realization, crystals for Demazure modules of affine Lie algebras of types $A^{(1)}_n,B^{(1)}_n,C^{(1)}_n,D^{(1)}_n, A^{(2)}_{2n-1},A^{(2)}_{2n}, and D^{(2)}_{n+1}$. We find a special sequence of affine Weyl group elements for the selected perfect crystal, and show if the highest weight is $l\La_0$, the Demazure crystal has a remarkably simple structure.
We study the path realization of Demazure crystals related to solvable lattice models in statistical mechanics. Various characters are represented in a unified way as the sums over one dimensional configurations which we call unrestricted, classically restricted and restricted paths. As an application characters of Demazure modules are obtained in terms of $q$-multinomial coefficients for several level 1 modules of classical affine algebras.
We review the path realization of Demazure crystals and discuss Demazure characters in the light of symmetric functions.