On some noncommutative algebras related to K-theory of flag varieties, part I
| dc.creator | Kirillov, Anatol N. | |
| dc.creator | Maeno, Toshiaki | |
| dc.date | 2005-04-14 | |
| dc.date | 2006-02-15 | |
| dc.date.accessioned | 2026-07-07T06:39:47Z | |
| dc.date.available | 2026-07-07T06:39:47Z | |
| dc.description | For any Lie algebra of classical type or type $G_2$ we define a $K$-theoretic analog of Dunkl's elements, the so-called truncated {\it Ruijsenaars-Schneider-Macdonald elements}, $RSM$-elements for short, in the corresponding {\it Yang-Baxter group}, which form a commuting family of elements in the latter. For the root systems of type $A$ we prove that the subalgebra of the {\it bracket algebra} generated by the RSM-elements is isomorphic to the Grothendieck ring of the flag variety. In general, we prove that the subalgebra generated by the {\it images} of the RSM-elements in the corresponding {\it Nichols-Woronowicz algebra} is canonically isomorphic to the Grothendieck ring of the corresponding flag varieties of classical type or of type $G_2$. In other words, we construct the ``Nichols-Woronowicz algebra model'' for the Grothendieck Calculus on Weyl groups of classical type or type $G_2,$ providing a partial generalization of some recent results by Y. Bazlov. We also give a conjectural description (theorem for type $A$) of a commutative subalgebra generated by the {\it truncated RSM-elements} in the bracket algebra for the classical root systems. Our results provide a proof and generalizations of recent conjecture and result by C. Lenart and A. Yong for the root system of type $A$. | |
| dc.identifier | https://arxiv.org/abs/math/0504290 | |
| dc.identifier | http://arxiv.org/abs/math/0504290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101206 | |
| dc.subject | Combinatorics | |
| dc.title | On some noncommutative algebras related to K-theory of flag varieties, part I | |
| dc.type | text |