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Title:
Unitary Representations of Simple Groups over Semifields
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Abstract:
The totally nonnegative matrices with determinant 1 can be considered as SL(n) over the semifield of non-negative real numbers. In this talk, we will discuss unitary representations of simple groups over semifields. We will give a classification of irreducible representations of SL(2) over the discrete tropical field and give a new family of dual pairs. Relations with scattering systems and zeta functions will also be discussed.
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