Orthogonal Stochastic Duality Functions from Lie Algebra Representations
Wolter Groenevelt (TU Delft - Analysis)
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Abstract
We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between ∗-representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and su(1,1). Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes.
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