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Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Krzysztof Nowak (1996)

Studia Mathematica

We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions g P g , ϕ , where for a fixed function ϕ, P g , ϕ denotes the one-dimensional orthogonal projection on the function U g ϕ , U is a group representation and g is an element of the group. They are defined as integrals ʃ W P g , ϕ d g , where W is an open, relatively...

Miura opers and critical points of master functions

Evgeny Mukhin, Alexander Varchenko (2005)

Open Mathematics

Critical points of a master function associated to a simple Lie algebra 𝔤 come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra t 𝔤 . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms...

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