Kazuto Iijima (飯島 和人/名大・PD)
On a higher level extension of Leclerc-Thibon product theorem in q-deformed Fock spaces
The q-deformed Fock spaces of higher levels were introduced by Jimbo-Misra-Miwa-Okado. Uglov defined a canonical bases in q-deformed Fock spaces of higher levels. Leclerc-Thibon showed a product theorem in
q-deformed Fock spaces of level one. The product theorem is regarded as a formal q-analogue of the tensor product theorem of level one. In this talk, we show a higher level analogue of Leclerc-Thibon product theorem under a suitable multi charge condition.
Masato Kobayashi (小林 雅人/埼玉大・理)
Combinatorial inequalities of Kazhdan-Lusztig polynomials in Bruhat graphs
In terms of Bruhat graphs, we establish combinatorial inequalities on q=1 values of KL polynomials for crystallographic Coxeter systems: Based on the author's recent result on the existence of a strict inequality of KL polynomials, we give a lower bound of their q=1 values by graph-theoretic distance.