Related papers: Springer theory in braid groups and the Birman-Ko-…

Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular,…

We use the Taylor-Wiles-Kisin patching method to prove some new cases of the Breuil-Schneider conjecture.

In the present paper we define dual monoids for all Artin-Tits groups and we prove that for the type $\tilde A_n$ we get a (quasi)-Garside structure. Such a structure provides normal forms for the Artin-Tits group elements and allows to…

In the 1920's Artin defined the braid group in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is…

We use some Lie group theory and Budney's unitarization of the Lawrence-Krammer representation, to prove that for generic parameters of definite form the image of the representation (also on certain types of subgroups) is dense in the…

Defined on Birman-Ko-Lee monoids, the rotating normal form has strong connections with the Dehornoy's braid ordering. It can be seen as a process for selecting between all the representative words of a Birman-Ko-Lee braid a particular one,…

We show that the simple elements of the dual Garside structure of an Artin group of type $D_n$ are Mikado braids, giving a positive answer to a conjecture of Digne and the second author. To this end, we use an embedding of the Artin group…

We define a Young subgroup of the braid group as a subgroup generated by an arbitrary subset of the Birman-Ko-Lee generators. We give an intrinsic description of such subgroups which yields, in particular, an easy criterion to decide…

Chiral conformal blocks in a rational conformal field theory are a far going extension of Gauss hypergeometric functions. The associated monodromy representations of Artin's braid group capture the essence of the modern view on the subject,…

We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. We…

We have results about the centralizer.

Two basic results on the S-rings over an abelian group are the Schur theorem on multipliers and the Wielandt theorem on primitive S-rings over groups with a cyclic Sylow subgroup. None of these theorems is directly generalized to the…

In the present paper we construct braid group actions on quantum symmetric pair coideal subalgebras of type AIII/AIV. This completes the proof of a conjecture by Kolb and Pellegrini in the case where the underlying Lie algebra is…

In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad…

We introduce framed versions of the $L$-moves and prove a one move theorem for the extension of the Markov theorem for framed braids. We further introduce framed versions of the Hilden and Pure Hilden groups, we give presentations and we…

The sequence of rings $H^n, n\ge 0,$ introduced in math.QA/0103190, controls categorification of the quantum sl(2) invariant of tangles. We prove that the center of $H^n$ is isomorphic to the cohomology ring of the (n,n) Springer variety…

We formulate an analogue of the Breuil-M\'ezard conjecture for the group of units of a central division algebra over a $p$-adic local field, and we prove that it follows from the conjecture for $\mathrm{GL}_n$. To do so we construct a…

Building further on work of Marin and Wagner, we give a cubic braid-type skein theory of the Links--Gould polynomial invariant of oriented links and prove that it can be used to evaluate any oriented link, adding this polynomial to the list…

We identify the dimension of the centralizer of the symmetric group $\mathfrak{S}_d$ in the partition algebra $\mathcal{A}_d(\delta)$ and in the Brauer algebra $\mathcal{B}_d(\delta)$ with the number of multidigraphs with $d$ arrows and the…

We generalize the Bernstein-Sato polynomials of Budur, Mustata and Saito to ideals in normal semigroup rings. In the case of monomial ideals, we also relate the roots of the Bernstein-Sato polynomial to the jumping coefficients of the…