Let $B_n$ be the braid group on $n$ strands, with the usual generators: $s_1, \ldots, s_{n-1}$ and their inverses, where $s_i$ is a positive half-twist interchanging the strands la …

The full braid group on $n$ strands $B_n$ admits a surjective homomorphism $p\colon\thinspace B_n\to \Sigma_n$ onto the symmetric group on $n$ letters, which takes a braid to the i …

This question was originally posted on math.SE by myself nearly a year ago. I've been thinking again about the problem after it recently received a little attention, but little pro …

Hello everyone, I have been trying (without success) to determine the following. Let $P$ denote the space of monic polynomials of degree $n$ with complex coefficients, which have …

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$, and let $U_q(\mathfrak{g})$ be some incarnation of the quantized universal enveloping algebra of $\ …

Consider the braid group $B_n$ presented in terms of the usual Artin generators $\sigma_1,\ldots,\sigma_{n-1}$. Now add the additional relations $\sigma_i^k = 1$ for $i=1,\ldots,n- …

Let $B_{2g+1}$ be the Artin braid group on $2g+1$ strands. There is a symplectic representation $\rho: B_{2g+1} \rightarrow Sp_{2g}(\mathbf{Z})$ called the "hyperelliptic repr …

I think this should be a 10 minute exercise in a decent computer algebra package - unfortunately I'm hopelessly ignorant of such things, so I'm putting it up here in the hope that …

At the end of Stephen Bigelow's paper "Braid Groups are Linear", he mentioned that there is a striking resemblance between the matrices of the Lawrence-Krammer (LK) representations …

Hi, i have read a statement from Sossinsky and Prasolov' s book "Knots, Lİnks, Braids and 3-Manifold", it says that two reduced word represent isotopic braids if and only if they …

I've been trying to google this question, but to no avail. The question sounds elementary but I hope it's suitable for the experts at MO! Let $B_n$ be the braid group on $n$-stran …

Let $f$ be a complex polynomial with an isolated singularity at the origin. Take a Morse deformation $\tilde{f}$, and consider the braid group action on the set of distinguished ba …

Let $B_n$ be the braid group on $n$ strands. It's a theorem of Daan Krammer and Stephen Bigelow that there is a a faithful representation $$B_n \to GL_{n \choose 2} \mathbb Z[t^{ …

Hi, I'm not very familiar with (even simple examples of) orbifolds, so my first question is: Let $C_2$ be $\mathbb{C}$ with one cone singularity at 0 of index 2. What is the f …

This is a question about Lusztig's theory of based modules. This theory is elementary but far from easy and is developed in Chapter 27 of "Introduction to quantum groups". Let $V$ …