OIF BERKELEY USA · OIF to Berkeley USA and Wuppertal Germany
6РП — Действия „Мария Кюри“
- Период
- 2005-09-01 → 2008-08-31
- Финансиране от ЕС
- 0 €
- Участници
- 2
- Схема
- OIF
Линиите свързват координатора с партньорите. За проекти отпреди 2014 г. CORDIS не винаги дава точни координати. Тези точки са на ниво град или държава.
Накратко на български
Теорията на представянията на квантовите афинни алгебри изследва сложни математически структури, като например специални полиноми и тензорни продукти. Тези изследвания помагат за развитието на математическата физика и разбирането на връзките между различни клонове на математиката.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Цел на проекта
The representation theory of quantum affine algebra is a fast growing, competitive field of research with many interactions with several branches in mathematics and mathematical physics. My past research in this field leads to new questions and perspectives that I intend to study: first I developed an algebraic approach to q,t-character, independent from the geometric construction of Nakajima. In particular it allows extending the construction of analogues of Kazhdan-Lustig polynomials and of the quantization of the Grothendieck ring to non-simply laced cases.Several problems remain open, such as a conjecture on the newly defined polynomials and the decomposition of tensor products. Then I developed the representation theory of general quantum affinizations, and in particular constructed a fusion procedure for the integrable representations. An associated tensor category has to be constructed. Besides I proved the Kirillov-Reshetikhin conjecture (1987) for all types; some relations between crystals of level 0 and Kirillov-Reshetikhin modules have still to be discovered. Several other new developments of this theory can also be expected.The department of mathematics of the University of California Berkeley (USA) (with E. Frenkel and N.i Reshetikhin), and the department of mathematics of the university of Wuppertal (Germany) (with P. Littelmann), would provide a wonderful scientific environment to pursue my researches: the theory of q-characters for finite dimensional representations of quantum affine algebras is one of the main tool of my phD and was introduced in the paper of Frenkel-Reshetikhin. This theory was then refined by Frenkel-Mukhin. Moreover the Kirillov-Reshetikhin conjecture that I proved was first stated in the paper with N. Reshetikhin as a co-author. Peter Littelmann is one of the funder of crystal theory, which has many applications in representation theory. This fellowship would allow creating long-term collaboration between the host institutions.
Оригинален текст от CORDIS (на английски).
Участници
- UNIVERSITY OF WUPPERTAL BERGISCHE UNIVERSITAT WUPPERTALКоординаторНиво градГермания
- UNIVERSITY OF CALIFORNIA, BERKELEYНиво граднепознат регион
Връзки
Данни: CORDIS, © Европейски съюз