Type: Seminar

Distribution: World

Expiry: 13 May 2011

Auth: athomas(.pmstaff;2039.2002)@p615.pc.maths.usyd.edu.au

The Algebra Seminar on Friday 13 May will be given by Anthony Henderson. Thank you to Anthony Henderson and Andrew Mathas for running the seminar during my absence. --------------------------------------------------------------------- Speaker: Anthony Henderson (University of Sydney) Date: Friday 13 May Time: 12.05-12.55pm Venue: Carslaw 175 Title: Mirabolic and exotic Robinson-Schensted correspondences Abstract: The Robinson-Schensted correspondence is an important bijection between the symmetric group S_n and the set of pairs of standard Young tableaux of the same shape with n boxes. By fixing one of the tableaux and letting the other vary, one obtains the left and right cells in the symmetric group. The correspondence can be defined by a simple combinatorial algorithm, but it also has a nice geometric interpretation due to Steinberg. S_n parametrizes the orbits of GL(V) in Fl(V) x Fl(V), where Fl(V) is the variety of complete flags in the vector space V of dimension n. The conormal bundle to an orbit O_w consists of triples (F_1,F_2,x) where (F_1,F_2) is in O_w and x is a nilpotent endomorphism of V which preserves both flags. The tableaux corresponding to w record the action of x on F_1 and F_2 for a generic triple in this conormal bundle. Roman Travkin gave a mirabolic generalization of the Robinson-Schensted correspondence, by considering the orbits of GL(V) in V x Fl(V) x Fl(V). Here S_n is replaced by the set of marked permutations (w,I) where w is in S_n and I is a subset of {1,...,n} such that if i<j, w(i)<w(j), and w(j) is in I, then w(i) is also in I. The other side of the correspondence, and the combinatorial algorithm, become suitably complicated. Peter Trapa and I found an exotic analogue of Travkin’s correspondence, resulting from the orbits of Sp(V) in V x Fl(V). I will explain Travkin’s results and our analogue. --------------------------------------------------------------------- Anne Thomas - anne.thomas@sydney.edu.au Seminar website - http://www.maths.usyd.edu.au/u/AlgebraSeminar/

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