6 problems

Macdonald's evaluation conjecture. For general parameters, the evaluation formula

Let $N$ be the number of variables, and let $a,b$ and pairs of parameters $(u_i,j_i)$ for $1\leq i\leq N$ specify the expected multivariate $q$-Racah type functions. Multivariate…

Let $V_{2j_1}(u)\tensor V_{2j_2}(u)$ be the tensor-product vector space, and let $(\mathcal{A}_2,\mathcal{A}_{12};\mathcal{B}_{12},\mathcal{B}_1)$ be the indicated ordered 4-tuple…

Let $R_i(z)$, for $i=0,1,-1$, be the polynomials defined by the determinant formula in equation (Ri2), together with the preceding definitions of their coefficients, and let…

Let $A,B$ be a tridiagonal pair over $\mathbb F$ having $q$-Racah type in the sense of Bockting-Conrad, and let $V$ be its underlying vector space. Let $\square_q$ denote the quant…

Shape conjecture. If $mathbb F$ is algebraically closed, then