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imported>Pythagoras0 (새 문서: ==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...) |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
| + | ==introduction== | ||
| + | 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== | ==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. | * 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. | ||
2015년 8월 24일 (월) 22:39 판
introduction
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.