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.