Level 0 Monomial Crystals

Monomial Crystals and Partition Crystals

Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal B(Λ0) for b sln, where the vertices are indexed by certain partitions. He showed that special cases of this construction agree with the Misra-Miwa realization and with Berg’s ladder crystal. Here we show that another special case is naturally isomorphic to a realization using Nakajima’s monomial c...

Highest Weights for Truncated Shifted Yangians and Product Monomial Crystals

Truncated shifted Yangians are a family of algebras which are natural quantizations of slices in the affine Grassmannian. We study the highest weight representations of these algebras. In particular, we conjecture that the possible highest weights for these algebras are described by product monomial crystals, certain natural subcrystals of Nakajima’s monomials. We prove this conjecture in type ...

0 Local cohomology , arrangements of subspaces and monomial ideals

If k is the field of complex numbers (or, more generally, a field of characteristic zero), the module H i I(R) is known to have a module structure over the Weyl algebra An(k), and one can therefore consider its characteristic cycle, denoted CC(H i I(R)) in this paper (see e.g. [2, I.1.8.5]). On the other hand, the arrangement X defines a partially ordered set P (X) whose elements correspond to ...

0 Geometric and Unipotent Crystals

Monomial Realization of Crystals B(∞) and B(λ) for Special Linear Lie Algebras

Nakajima introduced a certain set of monomials characterizing the irreducible highest weight crystals. The monomial set can be extended so that it contains B(∞) in addition to B(λ). We give explicit new realizations of the crystals B(∞) and B(λ) over special linear Lie algebras.