tailieunhanh - Báo cáo toán học: "The hook fusion procedure James Grime"

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: The hook fusion procedure James Grime. | The hook fusion procedure James Grime Department of Mathematics University of York York YO10 5DD UK jrg112@york. ac. uk Abstract We derive a new expression for the diagonal matrix elements of irreducible representations of the symmetric group. We obtain this new expression using Cherednik s fusion procedure. However instead of splitting Young diagrams into their rows or columns we consider their principal hooks. This minimises the number of auxiliary parameters needed in the fusion procedure. Submitted Feb 25 2005 Accepted Apr 25 2005 Published Jun 3 2005 Mathematics Subject Classifications 05E10 20C30 1 Introduction In this article we present a new expression for the diagonal matrix elements of irreducible representations of the symmetric group. We will obtain this new expression using Chered-nik s fusion procedure. This method originates from the work of Jucys J and has already been used by Nazarov and Tarasov N1 NT . However our approach differs by minimizing the number of auxiliary parameters needed in the fusion procedure. This is done by considering hooks of Young diagrams rather than their rows or columns as in N1 NT . Irreducible representations of the group Sn are parameterized by partitions of n CR . The Young diagram of a partition A is the set of boxes i j 2 Z2 such that 1 6 j 6 Ai. In drawing such diagrams we let the first coordinate i increase as one goes downwards and the second coordinate j increase from left to right. For example the partition A 3 3 2 gives the diagram If i j is a box in the diagram of A then the i j -hook is the set of boxes in A i j j j u i j i i We call the i i -hook the ith principal hook. THE ELECTRONIC JOURNAL OF COMBINATORICS 12 2005 R26 1 A standard tableau A is a filling of the diagram A in which the entries are the numbers 1 to n each occurring once. The Young Symmetrizer of a standard tableau A of shape A generates an irreducible CSn-module CR denoted Vx. In 1986 Ivan Cherednik proposed another description of the Young .