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Maud De Visscher

Publications and source records attributed to Maud De Visscher.

16 recordsLinked to original sources
arXiv2026

The orientifold Temperley--Lieb algebra

We construct gradings on the simple modules of 2-boundary Temperley--Lieb algebras and symplectic blob algebras by realising the latter algebras as quotients of Varagnolo--Vasserot's orientifold quiver Hecke algebras. We prove that the symplectic blob algebras are graded cellular and provide a conjectural algorithm for calculating their graded decomposition matrices. In doing so, we give the first explicit family of finite-dimensional graded quotients of the orientifold quiver Hecke algebras, providing a new entry point for the structure of these algebras -- in the spirit of Libedinsky--Plaza's ``blob algebra approach'' to modular representation theory.

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arXiv2025

The anti-spherical Hecke categories for Hermitian symmetric pairs

We calculate the $p$-Kazhdan--Lusztig polynomials for Hermitian symmetric pairs and prove that the corresponding anti-spherical Hecke categories categories are standard Koszul. We prove that the combinatorial invariance conjecture can be lifted to the level of graded Morita equivalences between subquotients of these Hecke categories.

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arXiv2024

The center of the walled Brauer algebra $B_{r,1}(δ)$

We show that the centre of the walled Brauer algebra $B_{r,1}(δ)$ over the complex field $\mathbb{C}$, for any parameter $δ\in \mathbb{C}$, is generated by the supersymmetric polynomials evaluated at the Jucys-Murphy elements. Moreover, we prove that its dimension is independent of the parameter $δ$.

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arXiv2021

Defining an Affine Partition Algebra

We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we show that it extends the Schur-Weyl duality between the symmetric group and the partition algebra. We also relate it to the affine partition category recently defined by J. Brundan and M. Vargas. Moreover, we show that this affine partition category is a full monoidal subcategory of the Heisenberg category.

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arXiv2013

The partition algebra and the Kronecker coefficients

We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition algebra. Our analysis leads to a uniform description of the Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition.

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arXiv2012

On Brauer algebra simple modules over the complex field

This paper gives two results on the simple modules for the Brauer algebra over the complex field. First we describe the module structure of the restriction of all simple modules. Second we give a new geometrical interpretation of Ram and Wenzl's construction of bases for the 'δ-permissible' simple modules.

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arXiv2010

Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra

We determine the decomposition numbers for the Brauer and walled Brauer algebra in characteristic zero in terms of certain polynomials associated to cap and curl diagrams (recovering a result of Martin in the Brauer case). We consider a second family of polynomials associated to such diagrams, and use these to determine projective resolutions of the standard modules. We then relate these two families of polynomials to Kazhdan-Lusztig theory via the work of Lascoux-Schützenberger and Boe, inspired by work of Brundan and Stroppel in the cap diagram case.

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arXiv2008

Alcove geometry and a translation principle for the Brauer algebra

There are similarities between algebraic Lie theory and a geometric description of the blocks of the Brauer algebra in characteristic zero. Motivated by this, we study the alcove geometry of a certain reflection group action. We provide analogues of translation functors for a tower of recollement, and use these to construct Morita equivalences between blocks containing weights in the same facet. Moreover, we show that the determination of decomposition numbers for the Brauer algebra in characteristic zero can be reduced to a study of the block containing the weight 0. We define parabolic Kazhdan-Lusztig polynomials for the Brauer algebra and show in certain low rank examples that they determine standard module decomposition numbers and filtrations.

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arXiv2007

On the blocks of the walled Brauer algebra

We determine the blocks of the walled Brauer algebra in characteristic zero. These can be described in terms of orbits of the action of a Weyl group of type $A$ on a certain set of weights. In positive characteristic we give a linkage principle in terms of orbits of the corresponding affine Weyl group. We also classify the semisimple walled Brauer algebras in all characteristics.

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arXiv2006

A geometric characterisation of the blocks of the Brauer algebra

We give a geometric description of the blocks of the Brauer algebra $B_n(δ)$ in characteristic zero as orbits of the Weyl group of type $D_n$. We show how the corresponding affine Weyl group controls the representation theory of the Brauer algebra in positive characteristic, with orbits corresponding to unions of blocks.

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