Related papers: The $0$-Rook Monoid and its Representation Theory

In 1986 Harer and Zagier computed a certain matrix integral to determine an influential closed-form formula for the number of (orientable) one-face maps on n vertices colored from N colors. Kerov (1997) provided a proof which computed the…

Given a continuous, odd, reducible and semi-simple $2$-dimensional representation $\bar\rho_0$ of $G_{\mathbb{Q},Np}$ over a finite field of odd characteristic $p$, we study the relation between the universal deformation ring of the…

Matrices over a finite field having fixed rank and restricted support are a natural $q$-analogue of rook placements on a board. We develop this $q$-rook theory by defining a corresponding analogue of the hit numbers. Using tools from coding…

We introduce a notion of $n$-commutativity ($0\le n\le \infty$) for cosimplicial monoids in a symmetric monoidal category ${\bf V}$, where $n=0$ corresponds to just cosimplicial monoids in ${\bf V,}$ while $n=\infty$ corresponds to…

It has been conjectured that the classical dynamics of M theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10.…

We introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new…

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…

Building on the work of P.N. Norton, we give combinatorial formulae for two maximal decompositions of the identity into orthogonal idempotents in the $0$-Hecke algebra of the symmetric group, $\mathbb{C}H_0(S_N)$. This construction is…

Combining the definition of 0-Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0-Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine…

Let $H=H_q(n)$ be the Hecke algebra of the symmetric group of degree n, over a field of arbitrary characteristic, and where q is a primitive l-th root of unity in $K$. Let $H_{\rho}$ be an l-parabolic subalgebra of $H$. We give an…

Let N be a square-free positive integer and let f be a newform of weight 2 on \Gamma_0(N). Let A denote the abelian subvariety of J_0(N) associated to f and let m be a maximal ideal of the Hecke algebra T that contains Ann_T(f) and has…

In the present paper we generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0,…

We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e. Baxter permutations, pairs of twin binary trees,…

Recently, Iwahori-Hecke algebras were associated to Kac-Moody groups over non-Archimedean local fields. In a previous paper, we introduced principal series representations for these algebras and partially generalized Kato's irreducibility…

We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$ for…

The groups G_{k,1} of Richard Thompson and Graham Higman can be generalized in a natural way to monoids, that we call M_{k,1}, and to inverse monoids, called Inv_{k,1}; this is done by simply generalizing bijections to partial functions or…

We consider the Kronecker quiver and determine the relations for the specialisation to q=0 of the generic composition algebra as well as those for Reineke's composition monoid. We also obtain a normal form for the varieties occurring in the…

We introduce a graded Hopf algebra based on the set of parking functions (hence of dimension (n+1)^{n-1} in degree n). This algebra can be embedded into a noncommutative polynomial algebra in infinitely many variables. We determine its…

We give a new formulation of Turing reducibility in terms of higher modalities, inspired by an embedding of the Turing degrees in the lattice of subtoposes of the effective topos discovered by Hyland. In this definition, higher modalities…

We construct irreducible graded representations of simply laced Khovanov-Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types…