Bitableaux Bases for the Diagonally Invariant Polynomial Quotient Rings

✍ Scribed by Edward E. Allen

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 352 KB
• Volume: 130
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1997.1652

✦ Synopsis

R: _P=P \_ # S n ] and let + and & be hook shape partitions of n. With 2 + (X, Y ) and 2 & (Z, W ) being appropriately defined determinants, x i being the partial derivative operator with respect to x i and P( )=P( x 1 , ..., x n , y 1 , ..., w n ), define

A basis is constructed for the polynomial quotient ring R Sn ÂI +, & that is indexed by pairs of standard tableaux. The Hilbert series of R Sn ÂI +, & is related to the Macdonald q, t-Kostka coefficients. 1997 Academic Press Let * be a partition of n (denoted by * | &n). Specifically, *= (* 1 , * 2 , ..., * k ) where n=* 1 +* 2 + } } } +* k , * i >0 for 1 i k and article no.