X=M for symmetric powers

By Anne Schilling, Mark Shimozono. 2004

48 citations recorded by the source corpus.

Author(s): Schilling, Anne; Shimozono, Mark | Abstract: The X=M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac--Moody algebra. In this paper we prove the X=M conjecture for tensor products of Kirillov--Reshetikhin crystals B^{1,s} associated to symmetric powers for all nonexceptional affine algebras.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/493a1a5c6d216f75aaf2e8555e4d7a8f7772328d

Citations in the corpus

• Crystal structure on rigged configurations (2005, unknown): “, D(b) = cc(Φ(b)) for all b ∈ P(B,Λ). Defining the generating functions X(B,Λ) = X b∈P(B,Λ) qD(b), M(L,Λ) = X (ν,J)∈RC(L,Λ) qcc(ν,J), (3.6) we get the immediate corollary of Theorem 3.1. Corollary3.2. [30, 37, 39] Let Λ, B and Las in Theorem 3.1. Then X(B,Λ) = M(L,Λ). 3.2. Crystal structure. In this ”