JOURNAL OF GEOMETRY AND PHYSICS 61(11) 2267-2284 2011年11月 [査読有り]
For a classical simple algebraic group G, we obtain the affirmative answer for the conjecture in Nakashima (2005)[3] that there exists an isomorphism between the geometric crystal on the flag variety and the one on the maximal uni potent subgroup ...
COMMUNICATIONS IN ALGEBRA 39(10) 3849-3865 2011年 [査読有り]
We present a one-to-one correspondence between the set of admissible pictures and the Littlewood-Richardson crystals. As a simple consequence, we shall show that the set of pictures does not depend on the choice of admissible orders.
Representation Theory 14(14) 446-509 2010年7月 [査読有り]
By modifying an earlier method of the authors (2008), certain affine geometric crystals are realized in affinization of the fundamental representation W(formula presented)l, and the tropical R maps for the affine geometric crystals are described e...
QUANTUM AFFINE ALGEBRAS, EXTENDED AFFINE LIE ALGEBRAS, AND THEIR APPLICATIONS 506(506) 215-226 2010年 [査読有り]
We shall realize certain affine geometric crystal of type D(4)((3)) associated with the fundamental representation W((w) over bar1) explicitly. By its explicit form, we see that it has a positive structure.
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 6(023) 14 2010年 [査読有り]
We introduce an epsilon system on a geometric crystal of type A(n), which is a certain set of rational functions with some nice properties. We shall show that it is equipped with a product structure and that it is invariant under the action of tro...
上智大学
理工学部