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Abstract

Abstract. We show that the specialization of nonsymmetric Macdonald polynomials at t = 0 are, up to multiplication by a simple factor, characters of Demazure modules for sl(n). This connection furnishes Lie-theoretic proofs of the nonnegativity and monotonicity of Kostka polynomials.

The number of flags in finite vector spaces: asymptotic normality and Mahonian statistics

“…The starting point should be Ion's article [9], which is a generalization of Sanderson's work [19], and one should also consider [11]. In view of (5.9) and [9,11], we propose the following conjecture: Note that (5.9) proves the case X = A.…”

“…Now, according to [6,Eq. (3.4)] and [19,Theorems 6 and 7], certain Demazure characters can be described via generalized Rogers-Szegő polynomials. …”

ON THE LAW OF LARGE NUMBERS FOR DEMAZURE MODULES OF $\widehat{\mathfrak{sl}}_2$

“…We will use Sanderson's formula for the real character of a Demazure module [10], which implies that the distribution of a − b with respect to µ N is given by 1 2 ) is the binomial distribution for N trials with success probability 1 2 . By unwinding Demazure's character formula [2, Lemma 3.6], we obtain…”

“…The outline of the proof of Theorem 7.1 and the organization of the paper is as follows: It is easy to show that the degree and the finite weight are uncorrelated. The covariance of the finite weight can be directly obtained from a known result by Sanderson about the real characters of Demazure modules [10]. Hence the main part is about the variance of the degree distribution.…”

Обобщенные Модули Вейля Для Скрученных Алгебр Токов

“…Модули Вейля для скрученных алгебр были введены в работе [2]. В статьях [8]- [10] было доказано, что характеры модулей Вейля для алгебр с простыми связями совпадают со специализациями несимметрических полиномов Макдональда в точке t = 0 [11], [12]. Мы вводим следующее обобщение модулей Вейля.…”