Hall-Littlewood functions and orthogonal polynomials (Q1814358)

The paper studies Hall-Littlewood functions \((HL\)-functions). A complex algebra \(A\) of symmetric polynomials of an infinite number of variables is considered. Then Hall-Littlewood functions are introduced as the result of a certain orthogonalization of the basis of the Schur functions. Three theorems are proved; they concern properties of these functions (among others their connection with automorphisms of the algebra \(A)\).