Categorification of tensor powers of the vector representation of Uq(gl(1|1))
Categorification of tensor powers of the vector representation of Uq(gl(1|1))
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DissertationPrüfungsdatum
30.05.2014Datum der Veröffentlichung
17.06.2014Erstgutachter
Stroppel, CatharinaZweitgutachter
Mazorchuk, VolodymyrMetadaten
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Inhalt
We consider the monoidal subcategory of finite-dimensional representations of Uq(gl(1|1)) generated by the vector representation, and we provide a graphical calculus for the intertwining operators, which enables to compute explicitly the canonical basis, as well as the action of Uq(gl(1|1)). We construct a categorification using graded subquotient categories of the BGG category O(gln) and graded functors between them (translation, Zuckermann’s and coapproximation functors). We describe then the regular blocks of these categories as modules over explicit diagram algebras, which are defined using Soergel modules and combinatorics of symmetric polynomials. We construct diagrammatically standard and proper standard modules for the properly stratified structure of these algebras.
Schlagwörter
Darstellungstheorie, Quantum-Gruppen, Alexander-Polynom, Kategorie O, Lie-Algebren, Representation theory, Quantum groups, Alexander polynomial, Category O, Lie algebras
Klassifikation (DDC)
510 MathematikSartori, Antonio: Categorification of tensor powers of the vector representation of Uq(gl(1|1)). - Bonn, 2014. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36359
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36359
@phdthesis{handle:20.500.11811/6104,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36359,
author = {{Antonio Sartori}},
title = {Categorification of tensor powers of the vector representation of Uq(gl(1|1))},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = jun,
note = {We consider the monoidal subcategory of finite-dimensional representations of Uq(gl(1|1)) generated by the vector representation, and we provide a graphical calculus for the intertwining operators, which enables to compute explicitly the canonical basis, as well as the action of Uq(gl(1|1)). We construct a categorification using graded subquotient categories of the BGG category O(gln) and graded functors between them (translation, Zuckermann’s and coapproximation functors). We describe then the regular blocks of these categories as modules over explicit diagram algebras, which are defined using Soergel modules and combinatorics of symmetric polynomials. We construct diagrammatically standard and proper standard modules for the properly stratified structure of these algebras.},
url = {https://hdl.handle.net/20.500.11811/6104}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36359,
author = {{Antonio Sartori}},
title = {Categorification of tensor powers of the vector representation of Uq(gl(1|1))},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = jun,
note = {We consider the monoidal subcategory of finite-dimensional representations of Uq(gl(1|1)) generated by the vector representation, and we provide a graphical calculus for the intertwining operators, which enables to compute explicitly the canonical basis, as well as the action of Uq(gl(1|1)). We construct a categorification using graded subquotient categories of the BGG category O(gln) and graded functors between them (translation, Zuckermann’s and coapproximation functors). We describe then the regular blocks of these categories as modules over explicit diagram algebras, which are defined using Soergel modules and combinatorics of symmetric polynomials. We construct diagrammatically standard and proper standard modules for the properly stratified structure of these algebras.},
url = {https://hdl.handle.net/20.500.11811/6104}
}
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