Degenerate Series Representations of the q-Deformed Algebra so'q(r,s)

• Дата: 2007
• Автор: Groza, V.A.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2007
• Назва видання: Symmetry, Integrability and Geometry: Methods and Applications
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/147377
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) / V.A. Groza // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ.

The q-deformed algebra so'q(r,s) is a real form of the q-deformed algebra Uq'(so(n,C)), n = r + s, which differs from the quantum algebra Uq(so(n,C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so'q(r,s). The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra so'q(r) × so'q(s) are given. Most of these representations are irreducible. Reducible representations appear under some conditions for the parameters determining the representations. All irreducible constituents which appear in reducible representations of the degenerate series are found. All *-representations of so'q(r,s) are separated in the set of irreducible representations obtained in the paper.