# Research

My interests lie in Representation Theory and Lie Theory. My advisor is Vyjayanthi Chari. Recently, she, along with several other authors, published a preprint of a result onto arxiv which defines a family of symmetric polynomials *G*_{ν, λ}(*z*, *q*), which they then show are the graded characters of an associated family of representations *M*(*ν*, *λ*) of the current algebra 𝔰𝔩_{n + 1}[*t*] that interpolate between level two Demazure modules and local Weyl modules. However, they only proved the formula true for certain “admissible” pairs of dominant integral weights (*ν*, *λ*). My research is to find new short exact sequences of representations of the current algebra that will expand such a graded character formula to all pairs of dominant integral weights.

Please click here for the website for the UCR Graduate Student Representation Theory Seminar.