Related papers: Rooted trees, Feynman graphs, and Hecke correspond…

In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more…

We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic…

Given a finitely aligned $k$-graph $\Lambda$, we let $\Lambda^i$ denote the $(k-1)$-graph formed by removing all edges of degree $e_i$ from $\Lambda$. We show that the Toeplitz-Cuntz-Krieger algebra of $\Lambda$, denoted by…

We give a presentation in terms of generators and relations of the cohomology in degree zero of the Campos-Willwacher graph complexes associated to compact orientable surfaces of genus $g$. The results carry a natural Lie algebra structure,…

In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra $H_n(q)$ of type $A_{n-1}$ in the non-generic case where $q$ is a root of unity. The approach is via the Specht modules of…

Cohen and Taylor introduced Plesken Lie algebras of finite groups and studied their structural properties. As a further step, we will introduce Plesken Lie algebra representations, Plesken Lie algebra modules and discuss the irreducibility…

We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…

Let $Q$ be a tree-type quiver, $\mathbf{k} Q$ its path algebra, and $\lambda$ a nonzero element in the field $\mathbf{k}$. We construct irreducible morphisms in the Auslander-Reiten quiver of the transjective component of the bounded…

We examine unitary and nonunitary representations of the Heisenberg-Weyl Lie algebra $\mathfrak{hw}_n$, with particular emphasis on tensor products of unitary representations and on indecomposable nonunitary representations. In the unitary…

We consider four classes of classical groups over a non-archimedean local field F: symplectic, (special) orthogonal, general (s)pin and unitary. These groups need not be quasi-split over F. The main goal of the paper is to obtain a local…

We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…

We prove that irreducible representations of the elliptic affine Hecke algebras of Ginzburg, Kapranov, and Vasserot are in one-to-one correspondence with certain nilpotent Higgs bundles on the elliptic curve. The main tool we use is the…

We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.

We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov's…

We interpret the construction of relative Cuntz-Pimsner algebras of correspondences in terms of the correspondence bicategory, as a reflector into a certain sub-bicategory. This generalises a previous characterisation of absolute…

In this paper we reformulate in a simpler way the combinatoric core of constructive quantum field theory We define universal rational combinatoric weights for pairs made of a graph and one of its spanning trees. These weights are nothing…

In this paper, we generalize the Dirac-dual-Dirac method to Hecke pairs with equivariant coarse embeddings and establish the K-theoretic isomorphisms between the maximal and reduced equivariant Roe algebras. We also extend these results to…

We give and study a construction of pre-Lie algebra structures on rooted trees whose edges and vertices are decorated, with a grafting product acting, through a map $\phi$, both on the decoration of the created edge and on the vertex that…

We study a class of representations called ``calibrated representations'' of the degenerate double affine Hecke algebra and those of the rational Cherednik algebra of type ${\mathrm{GL}}_n$. We give a realization of calibrated irreducible…

We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X_3] = X_5\}$ of Dixmier. First, we give a geometric…