Hecke algebras, difference operators, and quasi-symmetric functions
Quasi-symmetric functions and noncommutative symmetric functions are two recent generalizations of symmetric functions. The paper under review extends both of these concepts to Hall-Littlewood functions, defining quasi-symmetric Hall-Littlewood functions and noncommutative Hall-Littlewood functions. The development of these two functions parallels that of the ordinary Hall-Littlewood functions: the author first considers that Hall-Littlewood functions can be built up using Hecke algebras and Demazure's character formula [see \textit{G. Duchamp, D. Krob, A. Lascoux, B. Leclerc, T. Scharf} and \textit{J.-Y. Thibon}, Euler-Poincaré characteristic and polynomial representations of Iwashori-Hecke algebras, Publ. Res. Inst. Math. Sci. 31, No. 2, 179-201 (1995; Zbl 0835.05085)], and then extends these techniques to produce quasi-symmetric Hall-Littlewood functions. The author finally employs duality to derive the noncommutative Hall-Littlewood functions.
scientific article; zbMATH DE number 1545240
scientific article