Related papers: A new presentation for Specht modules with distinc…
We extend Grood's tableau construction of irreducible representations of the rook monoid and Steinberg's analogous result for the full transformation monoid. Our approach is characteristic-free and applies to any submonoid $\mathcal{M}(n)$…
We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.
We develop a unifying framework for the treatment of various persistent homology architectures using the notion of correspondence modules. In this formulation, morphisms between vector spaces are given by partial linear relations, as…
We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our…
The restriction of a (dual) Specht module to a smaller symmetric group has a filtration by (dual) Specht modules of this smaller group. In the cellular structure of the group algebra of the symmetric group, the cell modules are exactly the…
We consider the varieties of singular $m \times m$ complex matrices which may be either general, symmetric or skew-symmetric (with $m$ even). For these varieties we have shown in another paper that they had compact "model submanifolds", for…
Pseudoalgebras, introduced in [BDK], are multi-dimensional analogues of conformal algebras, which provide an axiomatic description of the singular part of the operator product expansion. Our main interest in this paper is the pseudoalgebra…
For a field of characteristic $\ne 2$ we study vector spaces that are graded by the weight lattice of a root system, and are endowed with linear operators in each simple root direction. We show that these data extend to a graded semisimple…
The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers…
We study persistence modules defined on commutative ladders. This class of persistence modules frequently appears in topological data analysis, and the theory and algorithm proposed in this paper can be applied to these practical problems.…
In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand (BGG) diagrams and complexes over cubical meshes of arbitrary dimension via the use of tensor-product structures of one-dimensional piecewise-polynomial…
We study a specific line arrangement obtained from a generic $2$-section of the braid arrangement, and compute the fundamental group of its complement via braid monodromy. We show that the resulting presentation of the fundamental group…
Let $p\geq 5$ be a prime number. In this paper, we construct Galois representations associated with modular forms for which the dimension of the $p$-torsion in the Bloch-Kato Selmer group can be made arbitrarily large. Our result extends…
We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method…
We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two…
Using combinatorial properties of symmetric polynomials, we compute explicitly the Soergel modules for some permutations whose corresponding Schubert varieties are rationally smooth. We build from them diagram algebras whose module…
We provide a recipe for building explicit representations of the real Clifford algebras once an explicit family is given in dimensions $1$ through $4$. We further give an explicit construction of spin coordinate systems for a given real…
We compute coherent presentations of Artin monoids, that is presentations by generators, relations, and relations between the relations. For that, we use methods of higher-dimensional rewriting that extend Squier's and Knuth-Bendix's…
In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of our efforts to extend in the noncompact…
We give new, short proofs of the presentations for the partition monoid and its singular ideal originally given in the author's 2011 papers in J Alg and IJAC.