From braces to Hecke algebras and quantum groups
نویسندگان
چکیده
We examine links between the theory of braces and set-theoretical solutions Yang–Baxter equation, fundamental concepts from quantum integrable systems. More precisely, we make connections with Hecke algebras identify new groups associated to set-theoretic coming braces. also construct a novel class discrete systems derive symmetries for corresponding periodic transfer matrices.
منابع مشابه
Quantum Drinfeld Hecke Algebras
We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the quantum setting over a field of arbitrary characteristic. We give necessary and sufficient conditions for such algebras to satisfy a Poincaré-Birkhoff-Witt proper...
متن کاملHecke algebras and involutions in Weyl groups
(Py,w;i ∈ N, u is an indeterminate) were defined and computed in terms of an algorithm for any y ≤ w in W . These polynomials are of interest for the representation theory of complex reductive groups, see [6]. Let I = {w ∈ W ;w2 = 1} be the set of involutions in W . In this paper we introduce some new polynomials P σ y,w = ∑ i≥0 P σ y,w;iu i (P σ y,w;i ∈ Z) for any pair y ≤ w of elements of I. ...
متن کاملBraid Groups and Iwahori-hecke Algebras
The braid group Bn is the mapping class group of an n-times punctured disk. The Iwahori-Hecke algebra Hn is a quotient of the braid group algebra of Bn by a quadratic relation in the standard generators. We discuss how to use Hn to define the Jones polynomial of a knot or link. We also summarize the classification of the irreducible representations of Hn. We conclude with some directions for fu...
متن کاملAffine Braid Groups and Hecke Algebras
These are notes for a class on double affine Hecke algebras and Macdonald polynomials given in the Fall of 2007 at the University of Minnesota. Here we introduce the (single and double) affine braid groups and Hecke algebras. We are following chapters 3,4, and 5 of Macdonald’s book [Mac]. There is also an (optional) aside giving applications to the T -equivariant K-theory of flag varieties G/B....
متن کاملin Algebra . Coxeter groups and Hecke algebras
The finite Coxeter groups are the finite groups generated by reflections on real Euclidean spaces. Examples include dihedral groups, the symmetry groups of regular polytopes (e.g. regular polygons and platonic solids) and the Weyl groups of semisimple complex Lie groups and Lie algebras (such as the special linear group and Lie algebra). General Coxeter groups may be defined as certain (special...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2022
ISSN: ['1793-6829', '0219-4988']
DOI: https://doi.org/10.1142/s0219498823501797