We study the way in which equivariant Kazhdan–Lusztig polynomials, inverse and Z-polynomials of matroids change under operation relaxation a collection stressed hyperplanes. This allows us to compute these polynomials for arbitrary paving matroids, we do number examples, including various associated with Steiner systems that admit actions Mathieu groups.

Let Z be a character of the symmetric group 5P~. The immanant of an n x n matrix A = [-a•] with respect to X is Zw~snZ(w)al,,~(t)...an, w~,). Goulden and Jackson conjectured, and Greene recently proved, that immanants of Jacobi-Trudi matrices are polynomials with nonnegative integer coefficients. This led one of us (Stembridge) to formulate a series of conjectures involving immanants , some of ...

Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles on toric varieties associated to GLn and G2. This can be considered of general interest and it improves the previously known results for these varieties. We...

The Lusztig Conjecture expresses the character of a finite-dimensional irreducible representation of a reductive algebraic group G in prime characteristic as a linear combination of characters of Weyl modules for G. The representations described by the conjecture are in one-to-one correspondence with the (finitely many) alcoves in the intersection of the dominant cone and the so-called Jantzen ...

This is the first paper to consider a mixed oligopoly in which a public Stackelberg leader competes with both domestic and foreign private firms. The welfare maximizing leader is shown to always produce less than under previous Cournot conjectures. Introducing leadership also alters previous public pricing rules resulting in prices that may be either greater than or less than marginal cost depe...

In [7], D. Kazhdan and G. Lusztig gave a conjecture on the multiplicity of simple modules which appear in a Jordan-H61der series of the Verma modules. This multiplicity is described in the terms of Coxeter groups and also by the geometry of Schubert cells in the flag manifold (see [8]). The purpose of this paper is to give the proof of their conjecture. The method employed here is to associate ...

We introduce two methods which reduce the checking of the joint relations on element pairs x, y (i.e., checking if μ(x, y) 6= 0, see 1.2) inside a two-sided cell of the symmetric group Sn to some special cases up to star operations. One involves the involutions in Sn, and the other involves the set Σλ for λ ∈ Λn (see 3.1 and 5.1). We give a detailed investigation for the properties of the set Σ...

The Hamiltonian of a recently proposed supersymmetric matrix model has been shown to become block-diagonal in the large-N , infinite ’t Hooft coupling limit. We show that (most of) these blocks can be mapped into seemingly non-supersymmetric (1 + 1)dimensional statistical systems, thus implying non-trivial (and apparently yet-unknown) relations within their spectra. Furthermore, the ground stat...