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.
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...
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;
Despite this, there is little evidence that actual or expected future sales
significantly affected asset prices. Graph 5 (centre and right-hand panels)
shows time series of price quotes for selected high-spread securitised assets,
distressed bonds and leveraged loans. True, the price of US leveraged loans
fell and spreads on some securitised assets rose after the EBA capital target
announcement, consistent with the deleveraging implications of this news.