BCn interpolation polynomials

introduction

notation

We also define relations $\prec$ and $\succ$ such that $\kappa\prec\lambda$ (equivalently $\lambda\succ\kappa$) for two partitions iff $\lambda/\kappa$ is a vertical strip; that is, $\kappa_i\le \lambda_i\le \kappa_i+1$ for all $i$.

branching rule

We have \[ \bar{P}^{*(n+1)}_\lambda(x_1,x_2,\dots x_n,v;q,t,s) = \sum_{\substack{\mu'\prec\lambda'\\\mu_{n+1}=0}} \psi^{(b)}_{\lambda/\mu}(v;q,t,s t^n) \bar{P}^{*(n)}_\mu(x_1,x_2,\dots x_n;q,t,s), \] where \[ \psi^{(b)}_{\lambda/\mu}(v;q,t,s) = \psi_{\lambda/\mu}(q,t) \prod_{(i,j)\in \lambda/\mu} (v+1/v-q^{j-1} t^{1-i}s-q^{1-j}t^{i-1}/s) \]

articles

• Rains, Eric M. “BCn-Symmetric Polynomials.” Transformation Groups 10, no. 1 (March 2005): 63–132. doi:10.1007/s00031-005-1003-y. http://arxiv.org/abs/math/0112035.
• Okounkov, A. “BC-Type Interpolation Macdonald Polynomials and Binomial Formula for Koornwinder Polynomials.” Transformation Groups 3, no. 2 (June 1998): 181–207. doi:10.1007/BF01236432.