Searcharxiv⌕ Search

arXiv subjects

Emily Norton

Publications and source records attributed to Emily Norton.

22 records · Page 2Linked to original sources
arXiv2016

Irreducible representations of rational Cherednik algebras for exceptional Coxeter groups, part II: some decomposition matrices of $H_c(E_8)$ and $H_c(F_4)$

This paper contains the decomposition matrices for blocks of defect at most $2$ in Category $\mathcal{O}_c(W)$ of the rational Cherednik algebra when $W=E_8$ or $F_4$ with equal parameters $c=1/d$, $d>2$ a regular number of $W$. A corollary of the result is a classification of the dimensions of support of the irreducible modules $L(τ)$ in $\mathcal{O}_{1/d}(W)$ except in the following cases: $W=E_8$, $d=4$ or $6$ and $L(τ)$ is in the principal block, or $d=2$ or $3$; $W=F_4$, $d=2$. In particular, this classifies the finite-dimensional modules of $H_c(E_8)$ when $d\neq 2,3,4,6$.

math.RT↗
arXiv2014

Irreducible representations of rational Cherednik algebras for exceptional Coxeter groups, Part I

This paper and its sequel describe the irreducible representations of the rational Cherednik algebra $H_c(W)$ for a finite Coxeter group $W$ of type $H_4$, $F_4$ with equal parameters, $E_6$, $E_7$, and $E_8$, when $c$ is not a half-integer. Herein appear the decomposition matrices of Category $\mathcal{O}_c(W)$ for $W=H_4$, $E_6$, and $E_7$, as well as a classification of finite-dimensional representations of $H_c(W)$ for these groups and for $H_c(F_4)$ with equal parameters.

math.RT↗
arXiv2013

Symplectic Reflection Algebras in Positive Characteristic as Ore Extensions

We investigate PBW deformations H of k[x,y]#G where G is the cyclic group of order p and k also has characteristic p; in these deformations, [x,y] takes a value in kG. These algebras are versions of symplectic reflection algebras that only exist in positive characteristic. They also happen to possess a presentation as an Ore extension over a commutative subring R, and via the derivation defining the extension, have interesting connections to certain polynomials appearing in combinatorics and related to alternating permutations (the André polynomials). We find the center of these algebras, their Verma modules, their simple modules, and the Ext groups between simples. The Verma modules coincide with the fibers of Mod H -->> Spec R, and Mod H turns out to be the disjoint union, in the sense of Smith and Zhang, of the Verma modules. As in non-defining characteristic, there are some distinctions between the t=0 and t=1 cases. We also obtain results when G is replaced with an elementary abelian p-group E: in particular, we find the center and the simple modules when [x,y] is in k[E].

math.RA↗