Hilbert Series

Given a permutation w ∈ Sn , we consider a determinantal ideal Iw whose generators are certain minors in the generic n × n matrix (filled with independent variables). Using ‘multidegrees’ as simple algebraic substitutes for torus-equivariant cohomology classes on vector spaces, our main theorems describe, for each ideal Iw : • variously graded multidegrees and Hilbert series in terms of ordinary and double Schubert and Grothendieck polynomials;

75p noel_noel 17-01-2013 39 4   Download

An extension of the Littlewood Restriction Rule is given that covers all pertinent parameters and simplifies to the original under Littlewood’s hypotheses. Two formulas are derived for the Gelfand-Kirillov dimension of any unitary highest weight representation occurring in a dual pair setting, one in terms of the dual pair index and the other in terms of the highest weight.

40p tuanloccuoi 04-01-2013 46 7   Download

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: A Combinatorial Formula for the Hilbert Series of bigraded Sn-modules...

24p thulanh7 04-10-2011 50 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: Conjectured Combinatorial Models for the Hilbert Series of Generalized Diagonal Harmonics Modules...

64p thulanh5 12-09-2011 61 4   Download