arXiv 0801.28182008-01-18math.RT

Compound basis arising from the basic $A^{(1)}_{1}$-module

Kazuya Aokage, Hiroshi Mizukawa, Hiro-Fumi Yamada

备注：: 12 pages
DOI：: 10.1007/s11005-008-0248-5

英文摘要：

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Multiple basic hypergeometric transformation formulas arising from the balanced duality transformation

Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking certain limits of the balanced duality transformation. By combining some of them, some transformation formulas for $A_n$ basic hypergeometric series is given. They include some generalizations of Watson, Sears and ${}_8 W_7$ transformations.

2014-03-10math.CAmath.QAmath.RT

Schur function identities arising from the basic representation of $A^{(2)}_{2}$

A Lie theoretic interpretation is given for some formulas of Schur functions and Schur $Q$-functions. Two realizations of the basic representation of the Lie algebra $A^{(2)}_2$ are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson-fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.

2013-08-30math.COmath.RT

Finite dimensional algebras not arising as blocks of group algebras

We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and Sambale. In particular, we fully classify blocks with 16-dimensional basic algebra.

2023-01-25math.GRmath.RT

Compound basis for the space of symmetric functions

The aim of this note is to introduce a compound basis for the space of symmetric functions. Our basis consists of products of Schur functions and $Q$-functions. The basis elements are indexed by the partitions. It is well known that the Schur functions form an orthonormal basis for our space. A natural question arises. How are these two bases connected? In this note we present some numerical results of the transition matrix for these bases. In particular we will see that the determinant of the transition matrix is a power of 2. This is not a surprising fact. However the explicit formula involv…

2007-05-21math.COmath.RT

An identity of parabolic Kazhdan-Lusztig polynomials arising from square-irreducible modules

We show a precise formula, in the form of a monomial, for certain families of parabolic Kazhdan-Lusztig polynomials of the symmetric group. The proof stems from results of Lapid-Minguez on irreducibility of products in the Bernstein-Zelevinski ring. By quantizing those results into a statement on quantum groups and their canonical bases, we obtain identities of coefficients of certain transition matrices that relate Kazhdan-Lusztig polynomials to their parabolic analogues. This affirms some basic cases of conjectures raised recently by Lapid.

2018-09-10math.QAmath.RT