Alladi Ramakrishnan Hall

Bases for root spaces of Borcherds-Kac-Moody algebras

R. Venkatesh

IIT Madras

Let $G$ be the BKM algebra. We consider the roots of $G$ of the form $\sum_{i\in I} k_i\alpha_i$ with the $k_i\leq 1$ for real simple roots $\alpha_i$. We prove that the root multiplicities of these roots have a close relationship with the (multi-)chromatic polynomial of the graph of $G$. Using this relationship, we construct bases of the root spaces of $G$ associated to these roots. This is joint work with G. Arunkumar and Deniz Kus.