tailieunhanh - Báo cáo toán học: " Robinson-Schensted correspondence for the signed Brauer algebras"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Robinson-Schensted correspondence for the signed Brauer algebras. | Robinson-Schensted correspondence for the signed Brauer algebras M. Parvathi and A. Tamilselvi Ramanujan Institute for Advanced Study in Mathematics University of Madras Chennai-600 005 India Submitted Jan 31 2007 Accepted Jul 5 2007 Published Jul 19 2007 Mathematics Subject Classifications 05E10 20C30 Abstract In this paper we develop the Robinson-Schensted correspondence for the signed Brauer algebra. The Robinson-Schensted correspondence gives the bijection between the set of signed Brauer diagrams d and the pairs of standard bi-domino tableaux of shape A A1 A2 with Al 22f A2 2 Pf r where Pf r A A 2 n 2f ỗr whose 2 core is ỗr ỗr r r 1 . 1 0 for fixed r 0 and 0 f 2 . We also give the Robinson-Schensted for the signed Brauer algebra using the vacillating tableau which gives the bijection between the set of signed Brauer diagrams Vn and the pairs of d-vacillating tableaux of shape A 2 Pf r and 0 f p . We derive the Knuth relations and the determinantal formula for the signed Brauer algebra by using the Robinson-Schensted correspondence for the standard bi-dominotableau whose core is ỗr r n 1. 1 Introduction In PK it has been observed that the number of signed Brauer diagrams is the dimension of the regular representation of the signed Brauer algebra whereas by Artin-Wedderburn structure theorem the dimension of the regular representation is the sum of the squares of the dimension of the irreducible representations of the signed Brauer algebra which are indexed by partitions A 2 rf r where rf r A A 2 n 2f ốrI whose 2 core is A Jr r r 1 . 1 0 g for fixed r 0 and 0 f 2 . This motivated us to construct an explicit bijection between the set of signed Brauer diagrams Vn and the pairs of d-vacillating tableaux of shape A 2 Tf r for fixed r 0 and 0 f n . We also construct the Robinson-Schensted correspondence for the signed Brauer algebra which gives the bijection between the set of signed Brauer diagrams d and the pairs