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Twisted forms of the determinant

โœ Scribed by William C Waterhouse

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
878 KB
Volume
86
Category
Article
ISSN
0021-8693

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๐Ÿ“œ SIMILAR VOLUMES

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It is proved that Z~(a+/3)>~A(a)+A ([3). This inequality is generalised for certain symmetric functions defined by Littlewood. Let O(a +/3) = r~(,~+m t, --~,-,+1,,, kt, k2 ..... ~)1. Then we prove that D(a+/3)~>O(a)+O(/3). Here ~.1,/t2, ~-3 ..... ~ is a partition such that ~., >k,\_ l >-.. >~.2>hl.

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We assume that G is in general position, so any l hyperplanes intersect in a point and any l+1 hyperplanes have empty intersection. We call Q=> n i=1 : i a defining polynomial for G. Let S be the coordinate ring of V and identify S with the polynomial ring C[u 1 , ..., u l ]. Let 0 p [V ] denote the

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Let the column vectors of X: M\_N, M<N, be distributed as independent complex normal vectors with the same covariance matrix 7. Then the usual quadratic form in the complex normal vectors is denoted by Z=XLX H where L: N\_N is a positive definite hermitian matrix. This paper deals with a representat