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Lie Groups and Representation Theory
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2018/12/11
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Motoki Takigiku (the University of Tokyo)
A Pieri-type formula and a factorization formula for K-k-Schur functions
Motoki Takigiku (the University of Tokyo)
A Pieri-type formula and a factorization formula for K-k-Schur functions
[ Abstract ]
We give a Pieri-type formula for the sum of K-k-Schur functions \sum_{\mu\le\lambda}g^{(k)}_{\mu} over a principal order ideal of the poset of k-bounded partitions under the strong Bruhat order, which sum we denote by \widetilde{g}^{(k)}_{\lambda}. As an application of this, we also give a k-rectangle factorization formula \widetilde{g}^{(k)}_{R_t\cup\lambda}=\widetilde{g}^{(k)}_{R_t} \widetilde{g}^{(k)}_{\lambda}
where R_t=(t^{k+1-t}), analogous to that of k-Schur functions s^{(k)}_{R_t\cup \lambda}=s^{(k)}_{R_t}s^{(k)}_{\lambda}.
We give a Pieri-type formula for the sum of K-k-Schur functions \sum_{\mu\le\lambda}g^{(k)}_{\mu} over a principal order ideal of the poset of k-bounded partitions under the strong Bruhat order, which sum we denote by \widetilde{g}^{(k)}_{\lambda}. As an application of this, we also give a k-rectangle factorization formula \widetilde{g}^{(k)}_{R_t\cup\lambda}=\widetilde{g}^{(k)}_{R_t} \widetilde{g}^{(k)}_{\lambda}
where R_t=(t^{k+1-t}), analogous to that of k-Schur functions s^{(k)}_{R_t\cup \lambda}=s^{(k)}_{R_t}s^{(k)}_{\lambda}.
