A multiplicative property of quantum flag minors
Caldero, Philippe
HAL, hal-00119977 / Harvested from HAL
Text on HAL
We study multiplicative properties of the (quantum) dual canonical basis B* associated to a semi-simple complex Lie group G. We provide a subset D of B* such that the following property holds : if two elements b, b' in B* q-commute and if one of these elements is in D, then the product bb' is in B* up to a power of q, where q the quantum parameter. If G is SL_n, then D is the set of so-called quantum flag minors and we obtain a generalization of a result of Leclerc-Nazarov-Thibon, see ArXiv:Math.QA/0011074.
Publié le : 2004-07-05
Classification:  [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT],  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] 
@article{hal-00119977,
     author = {Caldero, Philippe},
     title = {A multiplicative property of quantum flag minors},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00119977}
}

Caldero, Philippe. A multiplicative property of quantum flag minors. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00119977/