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Weight q-multiplicities for Representations of Lie Algebra C_3 by Maria Rodriguez Hertz ’21

Mon, May 3rd, 2021
1:00 pm
- 1:40 pm

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Weight q-multiplicities for Representations of Lie Algebra C3 by Maria Rodriguez Hertz ’21, Mathematics Senior Thesis Defense, Monday, May 3, 1 – 1:40 pm, live talk can be accessed at https://williams.zoom.us/j/97617951870.

Abstract:  Consider the following motivating question:  What is the number of ways that we can purchase n chicken nuggets given that you can only buy chicken nuggets in boxes of 6 and 9 pieces?

You have encountered a partition function!

If instead of nuggets you have a vector b which you want to write as a nonnegative sum of vector in a finite set of X, we can ask the same question:  In how many ways can we write b as a nonnegative sum of the vectors in X?  This is called a vector partition function problem.

In this thesis, we consider a vector partition function due to Kostant with applications to the representation theory of the Lie algebra C3. Our results include giving a q-analog formula for this vector partition function and we provide a related result describing the support of Kostant’s weight multiplicity formula, an alternating sum over a finite group whose terms involve Kostant’s partition function.

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