# G(l,k,d)-modules via groupoids

@article{Mazorchuk2014GlkdmodulesVG, title={G(l,k,d)-modules via groupoids}, author={Volodymyr Mazorchuk and Catharina Stroppel}, journal={arXiv: Representation Theory}, year={2014} }

In this note we describe a seemingly new approach to the complex representation theory of the wreath product $G\wr S_d$ where $G$ is a finite abelian group. The approach is motivated by an appropriate version of Schur-Weyl duality. We construct a combinatorially defined groupoid in which all endomorphism algebras are direct products of symmetric groups and prove that the groupoid algebra is isomorphic to the group algebra of $G\wr S_d$. This directly implies a classification of simple modules…

## Figures from this paper

## 10 Citations

Multiparameter colored partition category and the product of the reduced Kronecker coefficients

- Mathematics
- 2022

A BSTRACT . We introduce and study a multiparameter colored partition category CPar ( x ) by extending the construction of the partition category, over an algebraically closed ﬁeld 𝕜 of…

Representation Theory Of Algebras Related To The Bubble Algebra

- Mathematics
- 2016

In this thesis we study several algebras which are related to the bubble algebra, including the bubble algebra itself. We introduce a new class of multi-parameter algebras, called the multi-colour…

QUASI-SPLIT SYMMETRIC PAIRS OF $U(\mathfrak {gl}_N)$ AND THEIR SCHUR ALGEBRAS

- MathematicsNagoya Mathematical Journal
- 2020

Abstract We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like…

EXOTIC SPRINGER FIBERS FOR ORBITS CORRESPONDING TO ONE-ROW BIPARTITIONS

- MathematicsTransformation Groups
- 2020

We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the…

SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS

- MathematicsJournal of the Australian Mathematical Society
- 2016

We show how to use Jantzen’s sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of $\mathbf{U}_{q}$ -tilting modules (for any field $\mathbb{K}$ and any parameter…

Fiat categorification of the symmetric inverse semigroup $$\textit{IS}_n$$ISn and the semigroup $$F^*_n$$Fn∗

- Mathematics
- 2018

Starting from the symmetric group $$S_n$$Sn, we construct two fiat 2-categories. One of them can be viewed as the fiat “extension” of the natural 2-category associated with the symmetric inverse…

Handlebody diagram algebras

- Mathematics
- 2021

. In this paper we study handlebody versions of some classical diagram algebras, most prominently, handlebody versions of Temperley–Lieb, blob, Brauer, BMW, Hecke and Ariki–Koike algebras. Moreover,…

Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory

- MathematicsMathematische Zeitschrift
- 2018

We explain an elementary topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two…

Hall monoidal categories and categorical modules

- Mathematics
- 2016

We construct so called Hall monoidal categories (and Hall modules thereover) and exhibit them as a categorification of classical Hall and Hecke algebras (and certain modules thereover). The input of…

Cellular structures using $\textbf{U}_q$-tilting modules

- Mathematics
- 2015

We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a…

## References

SHOWING 1-10 OF 36 REFERENCES

2-row Springer Fibres and Khovanov Diagram Algebras for Type D

- MathematicsCanadian Journal of Mathematics
- 2016

Abstract We study in detail two row Springer fibres of even orthogonal type from an algebraic as well as a topological point of view. We show that the irreducible components and their pairwise…

A Frobenius Formula for the Characters of Ariki–Koike Algebras

- Mathematics
- 2000

Abstract Let H n, r be the Ariki–Koike algebra associated to the complex reflection group Wn, r = G(r, 1, n). In this paper, we give a new presentation of H n, r by making use of the Schur–Weyl…

The classical groups : their invariants and representations

- Mathematics
- 1940

In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from…

A Specht Module Analog for the Rook Monoid

- MathematicsElectron. J. Comb.
- 2002

This paper gives a combinatorial construction of the irreducible representations of the rook monoid, namely, the Specht modules.

Combinatorial Gelfand models for some semigroups and q-rook monoid algebras

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2009

Abstract Inspired by the results of Adin, Postnikov and Roichman, we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse…

Schur–Weyl Reciprocity for Ariki–Koike Algebras

- Mathematics
- 1999

Let g = glm1 ⊕ ··· ⊕ glmr be a Levi subalgebra of glm, with m = ∑ri = 1mi, and V the natural representation of the quantum group Uq(g). We construct a representation of the Ariki–Koike algebra Hn, r…

Irreducible representations of the generalized symmetric group Bmn

- MathematicsGlasgow Mathematical Journal
- 1987

This paper is devoted to the determining of the irreducible linear representations of the generalized symmetric group (elsewhere written as , Cm ≀ Sn or G(m, 1, n)) by considering the conjugacy…