Related papers: A note on certain finite-dimensional representatio…
We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. In cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give…
We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by…
We determine the finite groups whose real irreducible representations have different degrees.
This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of…
We consider the irreducible representations each of dimension 2 of the necklace braid group $\mathcal{NB}_n$ ($n=2,3,4$). We then consider the tensor product of the representations of $\mathcal{NB}_n$ ($n=2,3,4$) and determine necessary and…
A Coxeter group admits infinite-dimensional irreducible complex representations if and only if it is not finite or affine. In this paper, we provide a construction of some of those representations for certain Coxeter groups using some…
We prove that representations of the braid groups coming from weakly group-theoretical braided fusion categories have finite images.
We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…
Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we…
In 1996 E. Formanek classified all the irreducible complex representations of $B_n$ of dimension at most $n-1,$ where $B_n$ is the Artin braid group on $n$ strings. In this paper we extend this classification to the representations of…
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made…
In this paper we study irreducible matrix representations of the welded braid group $WB_n$, also known as the group of conjugating automorphisms of a free group $F_n.$ We prove that $WB_n$ has no irreducible representations of dimension…
We list the irreducible two dimensional complex representations of the Braid group B3 in elementary way. Then, we make a decomposition of the square of its irreducible Burau representation.
This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.
We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.
We study the problem of determining if the braid group representations obtained from quantum groups of types $E, F$ and $G$ at roots of unity have infinite image or not. In particular we show that when the fusion categories associated with…
We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite…
These are lecture notes from a lecture series given at CIRM in the Fall 2023. They give a down-to-earth introduction to Khovanov and Seidel's categorical representation of Artin-Tits groups, emphasizing the fact that it is all explicitly…
We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter's groups and the associated word problem, we turn to the…