Crystal Rules for (l,0)-JM Partitions

Function , and Their Crystal Theoretic Interpretation

In this paper we give an alternate combinatorial description of the " (ℓ, 0)-JM partitions " (see [4]) that are also ℓ-regular. Our main theorem is the equivalence of our combinatoric and the one introduced by James and Mathas ([7]). The condition of being an (ℓ, 0)-JM partition is fundamentally related to the hook lengths of the partition. The representation-theoretic significance of their com...

J un 2 00 9 Combinatorics of ( l , 0 ) - JM partitions , l - cores , the ladder crystal and the finite Hecke algebra

Jm Partitions and a Ladder Based Model for the Basic Crystal

In [1], Vazirani and I gave a new interpretation of what we called ℓ-partitions, also known as (ℓ, 0)-Carter partitions. The primary interpretation of such a partition λ is that it corresponds to a Specht module S λ which remains irreducible over the finite Hecke algebra Hn(q) when we specialize q to a primitive ℓ th root of unity. In [1], we relied heavily on the description of such a partitio...

(l, 0)-Carter Partitions and their crystal theoretic interpretation

In this paper we give an alternate combinatorial description of the “(l, 0)-Carter partitions”. Our main theorem is the equivalence of our combinatoric and the one introduced by James and Mathas (A q-analogue of the Jantzen-Schaper theorem). The condition of being an (l, 0)-Carter partition is fundamentally related to the hook lengths of the partition. The representation-theoretic significance ...

(l, 0)-Carter Partitions, their Crystal-Theoretic Behavior and Generating Function

In this paperwe give an alternate combinatorial description of the “(l, 0)-Carter partitions” (see [4]). The representation-theoretic significance of these partitions is that they indicate the irreducibility of the corresponding specialized Specht module over the Hecke algebra of the symmetric group (see [7]). Our main theorem is the equivalence of our combinatoric and the one introduced by Jam...