By Gert Almkvist, Robert Fossum (auth.), Marie-Paule Malliavin (eds.)

ISBN-10: 354008665X

ISBN-13: 9783540086659

ISBN-10: 3540359133

ISBN-13: 9783540359135

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Extra info for Séminaire d'Algèbre Paul Dubreil Proceedings, Paris 1976–1977 (30ème Année)

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EI Then get h~, (~,~) = ~ hl) ( ~ ) k ~ (~) ffi ~-11i =v ill =u 29 ei(~ )ei(~). kI h~ • 3O identity The h~ (~ ,~ ) = ~ Cauch~ Formula. 1o) ring formulas Define ~i a [31 , : B~> ~ i ). Then ted over ~ by the 1' by ~t ( ~ i ) ~-ring. the ~n(al) = a .... tz Consider (so the rk ~i = I for the subring ~ -operations. @-product Consider in § I so this ring n in fact is equal and ' interpretation. defined and all Clearly 4-----m another . , ~m] . is a aI ~ [a . B B by ~-ring. m ~ all form is one form of the ( ~ , ~ ) :IzI:~Y-"ez'(~ ) ez(~)" au These Another e l ( ~ ) el( ~ ) =~ IIi Then of this B genera- is again contains to A Suppose we co ® ~t(bl) : T-T i,j=1 (l + ~i ~jt).

2 (l_t2)n+I Example element Then A ffi B G ffi k[{XiXj} Ht(A) the n o n - i d e n t i t y S'(V) : gC:G} with g the H i l b e r t repre- over ~ . (V)G ) = iG[-1 ~ i gEG d e t ( l - g t ) Almkvist has calculated e l e m e n t s acting r e s u l t is on the r e g u l a r det(l-gt) where ord(g) the c h a r a c t e r i s t i c representation = (l-t°rdg)[ is the order ~(s) is the n u m b e r we can c a l c u l a t e G = ~ pm Gl/°rdg of the e l e m e n t H t ( S . ( v ) G ) ffi IGI-| where ~ we get a very nice of the group [Almkvist (1973)] .

3) Gn,r(X,Y) and t h e r e f o r e G Gaussian non-negative polynomial integers n,r Gn,r(X,Y) ; n~r, by : = (xn-yn)(xn-l-yn-l)'''(xn-r+l-yn-r+|) ( x r _ y r ) ( x r - l _ y r - l ) . . (X _ y) show i__~sh o m o g e n e o u s of de~ree = X n-r Gn_l,r_l (X,Y) n~r (X,Y) + yr G n _ l , r ( X , y ) is a p o l [ n o m i a l coefficients. ) l__~n ~[X,YJ ~t~ ~-[ j •o (This = Gn,r (Y'X) = Gn,n-r(X'Y)" we have (|-X r-J yJt) -! 3) above). 6. Suppose Gn+r,r(X,Y) = ~-" A p=o is the number of p a r t i t i o n s III = I o + l | + .

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Séminaire d'Algèbre Paul Dubreil Proceedings, Paris 1976–1977 (30ème Année) by Gert Almkvist, Robert Fossum (auth.), Marie-Paule Malliavin (eds.)

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