Alladi Ramakrishnan Hall

Gelfand-Tsetlin Patterns

S. Viswanath

IMSc

Gelfand-Tsetlin (GT) patterns are triangular arrays of
non-negative integers that satisfy certain inequalities. This talk
will be concerned with various aspects of GT patterns. We will show
that they can be identified with Young tableaux and that they describe
weights occurring in representations of the general linear group. We
also consider real-valued GT patterns, and show that they arise as
eigenvalue arrays of real symmetric matrices. Finally, we consider the
so-called GT polytope, and describe the solution to a special
quadratic maximization problem on this polytope.