By Kevin W. J. Kadell

ISBN-10: 0821825526

ISBN-13: 9780821825525

Macdonald and Morris gave a chain of continuing time period $q$-conjectures linked to root platforms. Selberg evaluated a multivariable beta style essential which performs a big function within the thought of continuing time period identities linked to root structures. Aomoto lately gave an easy and stylish evidence of a generalization of Selberg's essential. Kadell prolonged this evidence to regard Askey's conjectured $q$-Selberg necessary, which was once proved independently through Habsieger. This monograph makes use of a relentless time period formula of Aomoto's argument to regard the $q$-Macdonald-Morris conjecture for the foundation procedure $BC_n$. The $B_n$, $B_n^{\lor}$, and $D_n$ situations of the conjecture stick with from the concept for $BC_n$. a few of the information for $C_n$ and $C_n^{\lor}$ are given. This illustrates the elemental steps required to use tools given the following to the conjecture while the lowered irreducible root method $R$ doesn't have miniscule weight.

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Additional resources for A Proof of the Q-Macdonald-Morris Conjecture for Bcn

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N ), we have (723) =[i](i * l z l ) J J t . ,tn), + tv ,=i 2(*i,... 24), THE g-MACDONALD-MORRIS CONJECTURE FOR BCn 47 we obtain [ 1 U-\ ]"V t/-2 i %v r n*» UqbCnia^kltx,... 25) t=l = (qV'-2"-1* i=t/+l - ,(*•—»)*) f flCB,0,r-2(a, 6, *) + , - a » - i - ( - D * v BC n ,o,r(a, 6, k), 2,6,t,=^(1](i+i)n<, x qbcn(a,b, k\t2,... ,< v ,

S 25 V KEVIN W. J. 6) to ^-differentiate the factor (ti/tv)k(qtv/ii)k of qQ>n-i{k',t\,... , t n ) . 28) to effect the substitution t\ —• g

5. 27). 45). 45). Lemma 9. Let r > 1. 2) = 0, 20 , r (a, qbcn(a,b,k;t2,... ,*„,b>k) \ti — Q tv) . 8) == (tl+tv) ~ mW (t __ kt \ t v I I * * qbcn(a)b,k;t2l...

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A Proof of the Q-Macdonald-Morris Conjecture for Bcn by Kevin W. J. Kadell

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