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 Gν, λ(z, q), which they then show are the graded characters of an associated family of representations M(ν, λ) of the current algebra 𝔰𝔩n + 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.

Jonathan Dugan - Research

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 Gν, λ(z, q), which they then show are the graded characters of an associated family of representations M(ν, λ) of the current algebra 𝔰𝔩n + 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.