2014/06/05 by Hiraku Nakajima, Nakajima, Hiraku
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1406.1298
7 pages;ver.2 The claim that we have a geometric proof independent of the global crystal base is withdrawn; ver.3 minor revision
arxiv created 2014/07/05 · arxiv updated 2014/07/08
Cui (arXiv:1405.6441) has shown that the modified quantum affine algebra \widetilde\mathbf U (more precisely its quotients, BLN algebras) is affine cellular in the sense of Koenig and Xi. The proof is based on the structure of cells of \widetilde\mathbf U, studied previously in [http://arxiv.org/abs/math/0212253], the author's joint work with Beck. We here give more direct proof based on Lemma 6.17 in [http://arxiv.org/abs/math/0212253], together with a property of the bilinear form introduced in [http://arxiv.org/abs/math/0204183]. We also prove that cell ideals are idempotent, and hence Theorem 4.4 in [Koenig-Xi] is applicable.