منابع مشابه
Desingularization in the q-Weyl algebra
In this paper, we study the desingularization problem in the first qWeyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that s...
متن کاملFactorization of Z-homogeneous polynomials in the First (q)-Weyl Algebra
We present algorithms to factorize homogeneous polynomials in the first q-Weyl algebra and the first Weyl algebra. By homogeneous we mean homogeneous with respect to a Z-grading on the first (q-)Weyl algebra which will be introduced in this article. It turns out that the factorization can be almost completely reduced to commutative univariate factorization with some additional easy combinatoria...
متن کاملThe q-Weyl dimension formula
1 The Weyl dimension formula and its q-analogue This material is taken from notes for a joint paper with Zajj Daugherty and Rahbar Virk. Everything here is " well known ". Proposition 1.1. Let g be a finite dimensional complex semisimple Lie algebra etc.etc. ...???? Let ν be a dominant integral weight so that the irreducible module L(ν) of highest weight ν is finite dimensional. Letˆκ 1 = ν, ν ...
متن کاملInvolutive Bases in the Weyl Algebra
Involutive bases are a special kind of non-reduced Gröbner bases. They have been introduced by Gerdt and collaborators for polynomial ideals (see e.g. Zharkov and Blinkov, 1993; Gerdt and Blinkov, 1998a,b) based on ideas from the Janet–Riquier theory of differential equations (Janet, 1929; Riquier, 1910). Involutive bases possess special combinatorial properties: in particular, they define Stan...
متن کاملThe (Q, q)–Schur Algebra
In this paper we use the Hecke algebra of type B to define a new algebra S which is an analogue of the q–Schur algebra. We construct Weyl modules for S and obtain, as factor modules, a family of irreducible S–modules over any field.
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2018
ISSN: 0196-8858
DOI: 10.1016/j.aam.2018.02.005