Hermitian Symmetric Polynomials and CR Complexity

Kazhdan-lusztig Polynomials for Hermitian Symmetric Spaces

A nonrecursive scheme is presented to compute the KazhdanLusztig polynomials associated to a classical Hermitian symmetric space, extending a result of Lascoux-Schutzenberger for grassmannians. The polynomials for the exceptional Hermitian domains are also tabulated. All the KazhdanLusztig polynomials considered are shown to be monic.

Tropicalization, symmetric polynomials, and complexity

D. Grigoriev-G. Koshevoy recently proved that tropical Schur polynomials have (at worst) polynomial tropical semiring complexity. They also conjectured tropical skew Schur polynomials have at least exponential complexity; we establish a polynomial complexity upper bound. Our proof uses results about (stable) Schubert polynomials, due to R. P. Stanley and S. Billey-W. Jockusch-R. P. Stanley, tog...

Parabolic Kazhdan-lusztig Polynomials for Hermitian Symmetric Pairs

We study the parabolic Kazhdan-Lusztig polynomials for Hermitian symmetric pairs. In particular, we show that these polynomials are always either zero or a monic power of q, and that they are combinatorial invariants.

Hermitian Symmetric Domains

Then the V pq are obviously disjoint, and V pq = V . Further, the complex characters of S are exactly the z 7→ z−pz−qv, and any representation of S on a complex vector space has to break up into such characters, so V has to be the direct sum of the V . Conversely, if the V pq are given, then it is easy to define h : S → GL(V ) in terms of the above formula. We remark that V is homogeneous of we...

Laplace and Segal-bargmann Transforms on Hermitian Symmetric Spaces and Orthogonal Polynomials