TAILIEUCHUNG - Báo cáo toán học: "Crystal rules for (ℓ, 0)-JM partitions"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Crystal rules for (ℓ, 0)-JM partitions. | Crystal rules for 0 -JM partitions Chris Berg Fields Institute Toronto ON Canada cberg@ Submitted Jan 21 2010 Accepted Aug 18 2010 Published Sep 1 2010 Mathematics Subject Classifications 05E10 20C08 Abstract Vazirani and the author Electron. J. Combin. 15 1 2008 R130 gave a new interpretation of what we called -partitions also known as 0 -Carter partitions. The primary interpretation of such a partition A is that it corresponds to a Specht module Sx which remains irreducible over the finite Hecke algebra Hn q when q is specialized to a primitive 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 provided by James and Mathas. In this paper I use a new description of the crystal rege which helps extend previous results to all 0 -JM partitions similar to 0 -Carter partitions but not necessarily -regular by using an analogous condition for hook lengths which was proven by work of Lyle and Fayers. 1 Introduction The main goal of this paper is to generalize results of 3 to a larger class of partitions. One model of the crystal B Ao of 5Ỉe referred to here as reg has as nodes regular partitions. In 3 we proved results about where on the crystal regt a so-called -partition could occur. -partitions are the -regular partitions for which the Specht modules Sx are irreducible for the Hecke algebra Hn q when q is specialized to a primitive th root of unity. An -regular partition A indexes a simple module Dx for Hn q when q is a primitive ith root of unity. We noticed that within the crystal regt that another type of partitions which we call weak -partitions satisfied rules similar to the rules given in 3 for -partitions. In order to prove this we built an isomorphic version of the crystal regt which we denote laddt. The description of laddt with the isomorphism to regt can be found in 2 . Summary of results from this paper In Section 2 we give a new way of characterizing

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