scholarly journals Indecomposable Soergel bimodules for universal Coxeter groups

2016 ◽  
Vol 369 (6) ◽  
pp. 3883-3910 ◽  
Author(s):  
Ben Elias ◽  
Nicolas Libedinsky
Keyword(s):  
Coxeter Groups ◽  
Soergel Bimodules

Thicker Soergel calculus for B3

2019 ◽  
Vol 19 (12) ◽  
pp. 2050230
Author(s):  
Mitra Koley
Keyword(s):  
General Formula ◽  
Coxeter Group ◽  
Coxeter Groups ◽  
Explicit Calculation ◽  
Stepping Stone ◽  
Type Formula ◽  
Soergel Bimodules

Diagrammatic algebra provides a useful way to study Soergel bimodules. This approach proceeds via the simpler category [Formula: see text]Bim of Bott–Samelson bimodules, for which there is a well developed diagrammatic calculus. As Soergel bimodules are summands of Bott–Samelson bimodules, it is important to understand idempotents in the category [Formula: see text]Bim. For Coxeter groups of type [Formula: see text], we analyze this problem for certain important idempotents, namely, the idempotent projecting to the indecomposable Soergel bimodule corresponding to the longest element of the Coxeter group. We use a strategy analogous to one used by Elias in type [Formula: see text]. We present a full explicit calculation for the first nontrivial case [Formula: see text]. The strategy is applicable for general [Formula: see text] but much more involved. We hope that the [Formula: see text] case serves as a stepping stone for the general case.

scholarly journals Automorphisms of odd Coxeter groups

2021 ◽  
Author(s):  
Tushar Kanta Naik ◽  
Mahender Singh
Keyword(s):  
Coxeter Groups

scholarly journals The 300 “correlators” suggests 4D, $$ \mathcal{N} $$ = 1 SUSY is a solution to a set of Sudoku puzzles

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Aleksander J. Cianciara ◽  
S. James Gates ◽  
Yangrui Hu ◽  
Renée Kirk
Keyword(s):  
Coxeter Groups ◽  
Auxiliary Field ◽  
Permutation Groups ◽  
Weight Space ◽  
Field Problem ◽  
Truncated Octahedron ◽  
Color Problem ◽  
Minimal Representations

Abstract A conjecture is made that the weight space for 4D, $$ \mathcal{N} $$ N -extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups 𝕊d. Adinkras and Coxeter Groups associated with minimal representations of 4D, $$ \mathcal{N} $$ N = 1 supersymmetry provide evidence supporting this conjecture. It is shown that the appearance of the mathematics of 4D, $$ \mathcal{N} $$ N = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of 𝕊d.

Kazhdan-Lusztig cells in some weighted Coxeter groups

2017 ◽  
Vol 61 (2) ◽  
pp. 325-352 ◽  
Author(s):  
Jianyi Shi ◽  
Gao Yang
Keyword(s):  
Coxeter Groups

scholarly journals Divergence in right-angled Coxeter groups

2014 ◽  
Vol 367 (5) ◽  
pp. 3549-3577 ◽  
Author(s):  
Pallavi Dani ◽  
Anne Thomas
Keyword(s):  
Coxeter Groups
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