Lectures on Quantum Groups

Secant Dimensions of Minimal Orbits: Computations and Conjectures

“…We have implemented an algorithm for this based on the theory of crystal bases (cf. [20]). Roughly this works as follows.…”

On a q-analog of a Sahi result

“…In the sequel we are using standard results on finite dimensional U q k-modules of type 1, see [3]. As a U q k-module,…”

An Algorithm for Computing the Global Basis of a Finite Dimensional IrreducibleUq(so2n+1) orUq(so2n)-Module

“…In the sequel we need the following general lemma (see [3] p.32). Let V (l) be the irreducible U q (sl 2 )-module of dimension l + 1.…”

“…The reader is referred to [3] and [8] for basic definitions on crystal bases and crystal graphs. Given (L, B) and (L ′ , B ′ ) two crystal bases of the finite-dimensional…”