Alladi Ramakrishnan Hall

About the Horn Conjecture

V. S. Sunder

IMSc

We will discuss some of the story around the Horn Conjecture, which
is now actually theorem proved by Klyachko/Knutson-Tao. We shall try to trace
the history of this problem - what are the possible eigenvalue lists of
A+B in
terms of those of the self-adjoint matrices A and B. The fascinating story
starts with Weyl, eigenvalue inequalities, and finally reaches the happy
ending in such heady things as honeycombs, Clecsch-Gordon coeficients,...
In my talk, I shall emphasise the purely linear algebraic considerations that
led to the formulation by Horn of his celebrated conjecture.