Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0208138

Finite dimensional representations of rational Cherednik algebras

Yuri Berest·Pavel Etingof·Victor Ginzburg
View original source ↗Read source document ↗Export metadata ↓

Abstract

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine flag manifolds and Hilbert schemes are discussed.

Explore related subjects

math.RTmath.AGmath.QAmath.RA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yuri Berest, Pavel Etingof, Victor Ginzburg. 2002-09-04. Finite dimensional representations of rational Cherednik algebras. https://arxiv.org/abs/math/0208138

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the derived Hall algebra of a graded gentle one-cycle algebra I: the triangle structure

Under a mild condition, the perfect derived category and the finite-dimensional derived category of a graded gentle one-cycle algebra are described as twisted root categories of certain infinite quivers of type $\mathbb{A}_\infty^\infty$. As a consequence, it is shown that if $\ct$ is the perfect (respectively, finite-dimensional) derived category of such a graded gentle one-cycle algebra, then its triangle structure is up to triangle equivalence determined by the underlying additive category.

math.RT↗
arXiv2026

Towards Monoidal Categorifications of Twisted Products of Flag Varieties

Let $G$ be a simple, simply connected algebraic group of simply-laced type. For a positive braid word $β$ and $v\leδ(β)$, we study the cluster algebra associated with the twisted product of flag varieties $\mathring{\mathcal Z}_{v,β}$. We compare its Bao--Ye seed with a right-inductive weave seed and obtain local acyclicity and equality of the cluster and upper cluster algebras. Using Lusztig parameters in a bosonic extension algebra, we construct a monoidal subcategory $\mathscr C_{v,β}$ of a Hernandez--Leclerc category and prove that its Grothendieck ring contains the integral cluster algebra with noninvertible frozen variables. Every cluster monomial is the class of a real simple object of $\mathscr C_{v,β}$. The reverse inclusion, which would give a full monoidal categorification, is left as a conjecture.

math.RT↗
arXiv2026

Linear independence of global monomials on positive spaces

In this paper, we prove that global monomials on positive spaces are linearly independent, extending the basic fact that Laurent monomials in a Laurent polynomial algebra are linearly independent to a much more general setting. We also establish a global monomial avoidance phenomenon for positive spaces. Our approach is based on the study of Newton polytopes of Laurent expansions. These general results apply to positive spaces arising from cluster algebras (including the totally sign-skew-symmetric case), $Y$-patterns, and Laurent phenomenon algebras whose clusters are related by subtraction-free birational transformations. In particular, we obtain the proper Laurent monomial property and the linear independence of cluster monomials for all cluster algebras and Laurent phenomenon algebras under consideration. Notably, the proper Laurent monomial property follows from the global monomial avoidance phenomenon for positive spaces.

math.RT↗