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.
Original language | English |
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Pages (from-to) | 97-119 |
Number of pages | 23 |
Journal | Journal of Statistical Physics |
Volume | 174 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Stochastic duality
- Lie algebra representations
- Hypergeometric functions
- Orthogonal polynomials