Alexander polynomial and Koszul resolution.

Rosso, Marc

Displaying similar documents to “Alexander polynomial and Koszul resolution.”

A $q$ -analogue of the centralizer construction and skew representations of the quantum affine algebra.

Hopkins, Mark J., Molev, Alexander I. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On representation theory of quantum $S L_{q} (2)$ groups at roots of unity

Piotr Kondratowicz, Piotr Podleś (1997)

Banach Center Publications

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Irreducible representations of quantum groups $S L_{q} (2)$ (in Woronowicz’ approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the case of q being an odd root of unity. Here we find the irreducible representations for all roots of unity (also of an even degree), as well as describe “the diagonal part” of the tensor product of any two irreducible representations. An example of a not completely reducible representation is given. Non-existence of Haar functional is proved. The corresponding...

Quantum Racah coefficients and subrepresentation semirings.

Sage, Daniel S. (2005)

Journal of Lie Theory

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Junction type representations of the Temperley-Lieb algebra and associated symmetries.

Doikou, Anastasia, Karaiskos, Nikos (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Quantum symmetries in noncommutative C*-systems

Marcin Marciniak (1998)

Banach Center Publications

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We introduce the notion of a completely quantum C*-system (A,G,α), i.e. a C*-algebra A with an action α of a compact quantum group G. Spectral properties of completely quantum systems are investigated. In particular, it is shown that G-finite elements form the dense *-subalgebra of A. Furthermore, properties of ergodic systems are studied. We prove that there exists a unique α-invariant state ω on A. Its properties are described by a family of modular operators ${σ_{z}}_{z \in ℂ}$ acting on . It turns...

Left-covariant differential calculi on $S L_{q} (N)$

Konrad Schmüdgen, Axel Schüler (1997)

Banach Center Publications

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We study $N^{2} - 1$ dimensional left-covariant differential calculi on the quantum group $S L_{q} (N)$ . In this way we obtain four classes of differential calculi which are algebraically much simpler as the bicovariant calculi. The algebra generated by the left-invariant vector fields has only quadratic-linear relations and posesses a Poincaré-Birkhoff-Witt basis. We use the concept of universal (higher order) differential calculus associated with a given left-covariant first order differential calculus....