Pure Maths Colloquium: Highest weight vectors and transmutation
26 October 2015 16:00 in CM221
I will consider the problem of finding good bases for the highest weight vectors
for the polynomial functions on nxn matrices under the conjugation action in any characteristic. First we reduce this to finding good bases for the highest weight vectors for the polynomial functions on the nilpotent cone. Then we pass via “transmutation” to tuples of matrices. This leads to several interesting open problems. If time allows I will also indicate how one should extend these results to the exterior algebra of the nxn matrices in characteristic 0.
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