The nil-blob algebra: An incarnation of type $\tilde{A}_1$ Soergel calculus and of the truncated blob algebra

Soergel Calculus

The monoidal category of Soergel bimodules is an incarnation of the Hecke category, a fundamental object in representation theory. We present this category by generators and relations, using the language of planar diagrammatics. We show that Libedinsky's light leaves give a basis for morphism spaces and give a new proof of Soergel's classification of the indecomposable Soergel bimodules.

与三角矩阵相关的幂零分次代数及其在Soergel演算中的应用

Nil graded algebras associated to triangular matrices and their applications to Soergel Calculus

本文引入并研究了一类与Bott-Samelson双模自同态代数的Gelfand-Tsetlin子代数结构紧密相关的代数范畴，并发展了系列技术以获取图解式Soergel范畴中众多Gelfand-Tsetlin子代数的最优表示。

循环 nil- Brauer 和类型 D 的奇异 Soergel 双模

Cyclotomic nil-Brauer and Singular Soergel bimodules of type D

本文提出了一种新的单则范畴，通过构造从 cyclotomic nil-Brauer 分类到类型 D 的奇异 Soergel 双模的单则函子，并探讨了其在 Grothendieck 环上的同构性。

Soergel calculus and Schubert calculus

We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory.

$\tilde{A}_1$型Soergel calculus与nil-blob代数的分次和公式

Graded sum formula for $\tilde{A}_1$-Soergel calculus and the nil-blob algebra

本研究针对$\tilde{A}_1$型Soergel calculus代数，推广其与nil-blob代数的同构至双参数blob代数，结合Jones-Wenzl幂等元计算得到胞腔模双线性形式的对角化，进而证明Jantzen型滤过的分次和公式。

Hecke action on the principal block

In this paper we construct an action of the affine Hecke category (in its "Soergel bimodules" incarnation) on the principal block of representations of a simply-connected semisimple algebraic group over an algebraically closed field of characteristic bigger than the Coxeter number. This confirms a conjecture of G. Williamson and the second author, and provides a new proof of the tilting character formula in terms of antispherical $p$-Kazhdan-Lusztig polynomials.