Differential operators associated with zonal polynomials. II |
| |
Authors: | Donald St P Richards |
| |
Institution: | (1) University of the West Indies, UK;(2) Present address: the University of North Carolina, USA |
| |
Abstract: | Summary LetC
κ(S) be the zonal polynomial of the symmetricm×m matrixS=(sij), corresponding to the partition κ of the non-negative integerk. If ∂/∂S is them×m matrix of differential operators with (i, j)th entry ((1+δij)∂/∂sij)/2, δ being Kronecker's delta, we show that Ck(∂/∂S)Cλ(S)=k!δλkCk(I), where λ is a partition ofk. This is used to obtain new orthogonality relations for the zonal polynomials, and to derive expressions for the coefficients
in the zonal polynomial expansion of homogenous symmetric polynomials. |
| |
Keywords: | Primary 05A10 Secondary 33A30 33A65 |
本文献已被 SpringerLink 等数据库收录! |
|