Geometry and Category Realization of Lusztig Symmetry and Related Issues View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2016-2016

FUNDING AMOUNT

30000 CNY

ABSTRACT

The main research object in this project is to study the geometric and categorical realizations of Lusztig’s symmetries on quantized enveloping algebras and double Ringel-Hall algebras. Lusztig’s symmetries are very important in the study of quantized enveloping algebras. Geometrization is an important method to study canonical bases introduced by Lusztig, who realizes the positive part of a quantized enveloping algebra via the category of perverse sheaves on the representation space of some quiver. Categorification is also an important method to study canonical bases introduced by Khovanov-Lauda and Rouquire respectively, who realize the positive part of a quantized enveloping algebra via the category of projective modules of some algebra. We hope to study Lusztig’s symmetries by the methods of geometrization and categorification. First we shall give the geometric and categorical realizations of quantized enveloping algebras and double Ringel-Hall algebras. Then we shall give the geometric and categorical realizations of Lusztig’s symmetries on them by using the geometric realizations of Lusztig’s symmetries on the positive parts of quantized enveloping algebras. At last, we will give the geometric and categorical descriptions of the braid group relations. More... »

URL

http://npd.nsfc.gov.cn/projectDetail.action?pid=11526037

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