Test LaTex

In the age long tradition of such talks, we will begin by commenting on a few items from our CV. Then we turn to the math part which will be an excursion that begins with the canonical commutation relations i.e. the Heisenberg algebra ${\mathfrak h}_k$ in $k$ variables. We construct quadratic expressions in the generators of ${\mathfrak h}_{2n}$ that satisfy the Serre relations of $su(n,n)$. From tensor products of the unique irreducible unitary representation of ${\mathfrak h}_{2n}$ we then construct all unitary highest weight modules of $su(n,n)$. These representations will for small $k$ be missing some ${\mathfrak k}$ types, e.g. corresponding to all $(k+1)\times (k+1)$ minors. This means that there are homomorphisms between generalized Verma modules which in turn, by duality, leads to covariant differential operators. In the case of quantum groups, there is a similar picture. Here one begins with the Hayashi-Weyl algebra ${\mathcal H}{\mathcal W}_{2n}$.