Crystal rules for (ℓ, 0)-JM partitions

Chris Berg
unpublished
Vazirani and the author [Electron. J. Combin., 15 (1) (2008), R130] 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 H n (q) when q is specialized to a primitive ℓ th root of unity. To accomplish this we relied heavily on the description of such a partition in terms of its hook lengths, a condition
more » ... engths, a condition provided by James and Mathas. In this paper, I use a new description of the crystal reg ℓ which helps extend previous results to all (ℓ, 0)-JM partitions (similar to (ℓ, 0)-Carter partitions, but not necessarily ℓ-regular), by using an analogous condition for hook lengths which was proven by work of Lyle and Fayers.
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