SIMIS Summer Seminar: Totally Positive Operators and Unitary Representations of SL(2) over semifields

Speaker: Yongchang Zhu (Hong Kong University of Science and Technology)

Abstract: The infinite-dimensional analog of totally positive matrices is known as variation diminishing operators on function spaces. In the 1950s, I. Schoenberg classified variation diminishing operators of convolution type using Polya frequency functions. In the 1960s, I. Hirshman generalized this classification for Hankel convolution operators.

In this talk, we classify all irreducible unitary representations of SL(2) over some important semifields. We note that all representations are infinite dimensional. We show that each representation has a model in which the elements in SL(2) act as variation diminishing operators. The results from I. Hirshman’s work are utilized in the proof.

Additionally, we discuss some applications of our results.

Time: 12:00 ~ 13:30, Thu., June 20, 2024

Location: Floor 6, Innovation Center Building 3, Weicheng Road 62, Yangpu District, Shanghai, China

Zoom Meeting No.: 423 317 8953
Password: SIMIS

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