#### Alladi Ramakrishnan Hall

#### A bijection; a generalization of the Durfee square construction

#### B. Ravinder

##### IMSc

*It is known from the representation theory of the current algebra*

$sl_{r+1}[t]$ that given a positive integer $n$, there exist a bijection

from the set of partition overlaid Gelfand-Tsetlin patterns associated to

$n$ onto the set of partitions of $n$ into $r$ colors.

In this talk, we prove this by giving an explicit bijection. Our

construction may be viewed as a generalization of the Durfee square

construction. This talk is based on joint work with K.N. Raghavan and S.

Viswanath.

Done