Coxeter groups, symmetries, and rooted representations
نویسندگان
چکیده
منابع مشابه
Determinants of Representations of Coxeter Groups
In [APS17], the authors characterize the partitions of n whose corresponding representations of Sn have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups W . Namely, given a nontrivial multiplicative character ω of W , we give a closed formula for the number of irreducible representations of W with determinant ω. For Coxeter groups of type Bn a...
متن کاملCells and Representations of Right-angled Coxeter Groups
We study Kazhdan-Lusztig cells and corresponding representations of right-angled Coxeter groups and Hecke algebras associated with them. In case of the infinite groups generated by reflections of hyperbolic plane in the sides of right-angled polygons we obtain a complete explicit description of the left and two-sided cells. In particular, it appears that there are infinitely many left cells but...
متن کاملQuasiharmonic Polynomials for Coxeter Groups and Representations of Cherednik Algebras
We introduce and study deformations of finite-dimensional modules over rational Cherednik algebras. Our main tool is a generalization of usual harmonic polynomials for each Coxeter groups — the so-called quasiharmonic polynomials. A surprising application of this approach is the construction of canonical elementary symmetric polynomials and their deformations for all Coxeter groups.
متن کاملEssays on Coxeter groups Coxeter elements in finite Coxeter groups
A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
متن کاملRoot systems for asymmetric geometric representations of Coxeter groups
Root systems for asymmetric geometric representations of Coxeter groups Robert G. Donnelly1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 Abstract Results are obtained concerning root systems for asymmetric geometric representations of Coxeter groups. These representations were independently introduced by Vinberg and Eriksson, and generalize the standard ge...
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: Communications in Algebra
سال: 2017
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2017.1363221