D型仿射标志品种

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-03-14 DOI:10.1016/j.jalgebra.2025.02.043

Quanyong Chen, Zhaobing Fan, Qi Wang

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引用次数: 0

摘要

Hecke代数和仿射A型量子群分别承认局部域上的完全标志和部分标志的几何实现。在此基础上，建立了仿射D型完全（部分）标志变体的格表示，并确定了仿射D型完全标志变体的卷积代数的结构，该卷积代数与（扩展）仿射Hecke代数同构。我们还证明了卷积代数的单项式基和正则基的存在，并建立了正则基对乘法的正性质。

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Affine flag varieties of type D

The Hecke algebras and quantum group of affine type A admit geometric realizations in terms of complete flags and partial flags over a local field, respectively. Subsequently, it is demonstrated that the quantum group associated to partial flag varieties of affine type C is a coideal subalgebra of quantum group of affine type A. In this paper, we establish a lattice presentation of the complete (partial) flag varieties of affine type D. Additionally, we determine the structures of convolution algebra associated to complete flag varieties of affine type D, which is isomorphic to the (extended) affine Hecke algebra. We also show that there exists a monomial basis and a canonical basis of the convolution algebra, and establish the positivity properties of the canonical basis with respect to multiplication.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.