Laguerre and Meixner symmetric functions, and infinite-dimensional diffusion processes

Understand

The Laguerre symmetric functions introduced in the note are indexed by arbitrary partitions and depend on two continuous parameters.

• The top degree homogeneous component of every Laguerre symmetric function coincides with the Schur function with the same index.
• Thus, the Laguerre symmetric functions form a two-parameter family of inhomogeneous bases in the algebra of symmetric functions.
• These new symmetric functions are obtained from the N-variate symmetric polynomials of the same name by a procedure of analytic continuation.