\(D_7^{(1)}\)- Geometric Crystal at the Spin Node

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-03-12 DOI:10.1007/s10468-025-10325-w

Kailash C. Misra, Toshiki Nakashima, Suchada Pongprasert

引用次数: 0

Abstract

Let \(\mathfrak {g}\) be an affine Lie algebra with index set \(\varvec{I}\) = {0, 1, 2, \(\ldots , \varvec{n}\}\). It is conjectured that for each Dynkin node \(\varvec{k} \in \varvec{I} \setminus \{{\textbf {0}}\}\) the affine Lie algebra \(\mathfrak {g}\) has a positive geometric crystal. In this paper, we construct a positive geometric crystal for the affine Lie algebra \(\varvec{D}_{\textbf {7}}^{{\textbf {(1)}}}\) corresponding to the Dynkin spin node \(\varvec{k}= {\textbf {7}}\).

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\(D_7^{(1)}\)-旋转节点的几何晶体

设\（\mathfrak {g}\）是一个仿射李代数，其索引集\(\varvec{I}\) = {0,1,2, \（\ldots, \varvec{n}\}\）。我们推测，对于每一个Dynkin节点\(\varvec{k} \in \varvec{I} \setminus \{{\textbf{0}}\})，仿射李代数\（\mathfrak {g}\）都有一个正的几何晶体。本文构造了与Dynkin自旋节点\（\varvec{k}= {\textbf{7}}\）对应的仿射李代数\（\varvec{D}_{\textbf {7}}^{\textbf{(1)}}}）的正几何晶体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.