( q , t ) - analogues and GLn ( F q )
نویسنده
چکیده
Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to column-strict tableaux and Macdonald’s “7 variation” of Schur functions, the other relating to permutation statistics and Hilbert series from the invariant theory of GLn(Fq).
منابع مشابه
(q, t)-ANALOGUES AND GLn(Fq) VICTOR REINER AND
Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to col...
متن کاملBethe Subalgebras in Twisted Yangians
We study analogues of the Yangian of the Lie algebra glN for the other classical Lie algebras soN and spN . We call them twisted Yangians. They are coideal subalgebras in the Yangian of glN and admit homomorphisms onto the universal enveloping algebras U(soN ) and U(spN ) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular ...
متن کاملA (q, t)-BINOMIAL COEFFICIENT FOR GLn(Fq)
Abstract. We investigate a (q, t)-generalization of the usual binomial and q-binomial coefficients. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These polynomials and their interpretations generalize further in two directions, one relatin...
متن کاملEndoscopy and the cohomology of $GL(n)$
Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field. Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...
متن کاملA Relationship between the Major Index for Tableaux and the Charge Statistic for Permutations
The widely studied q-polynomial fλ(q), which specializes when q = 1 to fλ, the number of standard Young tableaux of shape λ, has multiple combinatorial interpretations. It represents the dimension of the unipotent representation Sλ q of the finite general linear group GLn(q), it occurs as a special case of the Kostka-Foulkes polynomials, and it gives the generating function for the major index ...
متن کامل