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

By Kevin W. J. Kadell

Macdonald and Morris gave a chain of continuing time period $q$-conjectures linked to root platforms. Selberg evaluated a multivariable beta sort critical which performs a major function within the concept of continuous time period identities linked to root platforms. Aomoto lately gave an easy and stylish facts of a generalization of Selberg's crucial. Kadell prolonged this facts to regard Askey's conjectured $q$-Selberg indispensable, which used to be proved independently via Habsieger. This monograph makes use of a continuing time period formula of Aomoto's argument to regard the $q$-Macdonald-Morris conjecture for the foundation approach $BC_n$. The $B_n$, $B_n^{\lor}$, and $D_n$ instances of the conjecture keep on with from the theory for $BC_n$. a few of the info for $C_n$ and $C_n^{\lor}$ are given. This illustrates the fundamental steps required to use tools given the following to the conjecture whilst the decreased irreducible root approach $R$ doesn't have miniscule weight.

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

**Example text**

37). 1) holds with r replaced by r — 1. 2) U * t w(ti,... '*») A n (a,6,fc;*i,... ,tn) (r r-3 3) =(

The following lemma explicitly expresses the geometry of the simple roots of Bn and Cn in terms of g 6c n (a,6, fe;ti,... ,* n )Lemma 6. g 6c n (a,6,fc;*2,-" ,*+i *J f l ( f ) a ( ^ ^ * i * l
*

We see that S y m ^ - i , tv) is symmetric in tv-\ and tv. 17) and s = *„_i, t = tVl Q = qk. 14), respectively. • The following lemma extends Lemma 10 from An-\ to Bn. Lemma 12. 18) T(j) be invariant under t <-+ l/t and have a Laurent expansion at t = 0. 19) [1] (1 + 1) (l - <)(1 - f ) T(<) = Q [1] (1 + < ) ( ! - 0(1 " j) T(0- Proof. 21) [l](l + i ) ( l - O T ( 0 = 0. 22) =[i](i + I)(i_0T(<)-Q[l]i(l = -Q[l}\(l + + I)(l-<)T(<) j)(l-t)T(t). 23) [i](i + i ) ( i - t ) ( i - 5 ) T ( o = g[i]<(i + y ) ( i - O T ( 0 = Q[l](l + t)(l-t)T(t).