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

By Kevin W. J. Kadell

ISBN-10: 0821825526

ISBN-13: 9780821825525

Macdonald and Morris gave a chain of continuous time period $q$-conjectures linked to root structures. Selberg evaluated a multivariable beta style quintessential which performs a tremendous position within the concept of continuing time period identities linked to root platforms. Aomoto lately gave an easy and stylish facts of a generalization of Selberg's imperative. Kadell prolonged this evidence to regard Askey's conjectured $q$-Selberg essential, which was once proved independently via 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 to from the theory for $BC_n$. a number of the information for $C_n$ and $C_n^{\lor}$ are given. This illustrates the fundamental steps required to use tools given right here to the conjecture while the decreased irreducible root process $R$ doesn't have miniscule weight.

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**Extra info for A Proof of the Q-Macdonald-Morris Conjecture for Bcn**

**Example text**

48) of ^e n (a,6, k\t\,... 29) and t = tni Q = qa. 26). • Lemmas 11 and 13 constitute the ^-transportation theory for Bn. The following lemma extends Lemma 10 from An-\ to C„. Lemma 14. 30) S(«) = S ( i ) be invariant under s <-* q/s and have a Laurent expansion at s = 0. 2Q [1] I (1 - X ) ( i _ Qs2) S(S). Proof. 32) [ 1 ] ( « - 2 ) S ( « ) = 0. 33) = [1] (s - £) S(«) - Q [1] * 2 (« - i ) S(«) = _Q[1]s2(s_£)S(S). Replacing s by g/s, we have [1] 5 (1 - 1 ) ( 1 - g s 2 ) S(«) = q2Q [1] 4 (« - *) S(«).

M ; * ! ,«„) = («-*-9(r-2)*),BC,Blo,r-2(a,6,t) + 9-8*-1-(r-1)*,5Cn,o1r(a,*,*). 3) gives ? 5) + ,-(2»-r-D* — qBCn,0,r-2(a, b, k) 2 » - l , f l C „ , o , r ( a , 6, * ) . 1). 4) of our (/-machine by the (/-transportation theory for BCn. ,tfn), m > l . 1). 4) of our 1. Taking u;(**n)- i=n — m - f l KEVIN W. J. -(m-i)*(1] n rj »'=n-m-f 2 - ,-("»-*)* [1] - J —
*

N ), we have (723) =[i](i * l z l ) J J t . ,tn), + tv ,=i 2*
*

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

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