Laguerre and Meixner orthogonal bases in the algebra of symmetric functions

TL;DR

This paper explores Laguerre and Meixner orthogonal bases within the algebra of symmetric functions, linking these mathematical structures to models of infinite-dimensional Markov dynamics, and providing detailed results expanding on previous work.

Contribution

It introduces and analyzes Laguerre and Meixner orthogonal bases in symmetric functions, connecting them to infinite-dimensional Markov processes, and offers detailed mathematical exposition of earlier announced results.

Findings

Development of Laguerre and Meixner bases in symmetric functions

Connection established with infinite-dimensional Markov dynamics

Provides detailed proofs and analysis of prior results

Abstract

Analogs of Laguerre and Meixner orthogonal polynomials in the algebra of symmetric functions are studied. This is a detailed exposition of part of the results announced in arXiv:1009.2037. The work is motivated by a connection with a model of infinite-dimensional Markov dynamics.