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Quantum Algebra papers

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Coherence Constraints for Operads, Categories and Algebras
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the…
Martin Markl, Steve ShniderJul 14, 2000
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Affine Sergeev Algebra and q-Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group
We study a q-deformation for the semi-direct product of the symmetric group Sn with the Clifford algebra on n anticommuting generators. We obtain a q-version of the projective analogue for…
Andrew Jones, Maxim NazarovMar 20, 2000
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Nonsymmetric Koornwinder polynomials and duality
Motivated by the work of Koornwinder, Macdonald, Cherednik, Noumi, and van Diejen we define a 6-parameter double affine Hecke algebra and establish its basic structural properties, including the…
Siddhartha SahiJul 1, 1999
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Capelli Identities for Classical Lie Algebras
We extend the Capelli identities (1890) from the Lie algebra glN to the other two classical Lie algebras soN and spN. We employ the theory of reductive dual pairs due to Howe. Our technique…
Alexander Molev, Maxim NazarovFeb 25, 1999
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On modules associated to coalgebra Galois extensions
For a given entwining structure (A,C)ψ involving an algebra A, a coalgebra C, and an entwining map ψ: C A A C, a category AC(ψ) of right (A,C)ψ-modules is defined…
Tomasz BrzezinskiOct 9, 1998
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Web bases for sl(3) are not dual canonical
We compare two natural bases for the invariant space of a tensor product of irreducible representations of A2, or sl(3). One basis is the web basis, defined from a skein theory called the…
Mikhail Khovanov, Greg KuperbergSep 28, 1998
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Exotic Differential Operators on Complex Minimal Nilpotent Orbits
Let O be the minimal nilpotent adjoint orbit in a classical complex semisimple Lie algebra g. O is a smooth quasi-affine variety stable under the Euler dilation action C* on g. The algebra of…
A. Astashkevich, R. BrylinskiJun 30, 1998
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Lie algebras and degenerate Affine Hecke Algebras of type A
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke…
T. Arakawa, T. SuzukiApr 21, 1998
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Degenerate Double Affine Hecke Algebra And Conformal Field Theory
We introduce a class of induced representations of the degenerate double affine Hecke algebra of glN and analyze their structure mainly by means of intertwiners. We also construct them from modules…
T. Arakawa, T. Suzuki, A. TsuchiyaApr 21, 1998
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qR-conformal symmetries in 2D nonlocal quantum field theory, categorical representation theory, and Virasoro algebra
The paper is devoted to the symmetry aspects of 2D nonlocal field theory, which is the simplest deformation of the conformally invariant quantum field theory with one free bosonic field. The inverse…
D. V. JurievApr 18, 1998
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Factorizable sheaves and quantum groups
The category C (studied by Andersen-Jantzen-Soergel) of representations of a Lusztig's small quantum group at a root of unity, together with its modular structure, is defined…
Roman Bezrukavnikov, Michael Finkelberg, Vadim SchechtmanApr 15, 1998
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Support varieties for quantum groups
For any module M over small quantum group one defines the support variety using construction from the theory of restricted Lie algebras. It is a closed conical subset of nilpotent cone of the…
V. OstrikFeb 9, 1998
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Quantum SL(3,C)'s with classical representation theory
We study and classify almost all quantum SL(3,C)'s whose representation theory is ``similar'' to that of the (ordinary) group SL(3,C). Only one case, related to smooth elliptic curves,…
Christian OhnJan 23, 1998
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Yangian Algebras and Classical Riemann Problems
We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation…
S. Khoroshkin, D. Lebedev, S. PakuliakJan 12, 1998
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The q-Fourier transform of q-distributions
We consider functions on the lattice generated by the integer powers of q2 for 0<q<1 and construct the q-analog of Fourier transform based on the Jackson integral in the space of distributions…
M. Olshanetsky, V. RogovJan 12, 1998
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Solutions of the qKZB Equation in Tensor Products of finite dimensional modules over the elliptic quantum group Eτ,ηsl2
We consider the quantized Knizhnik-Zamolodchikov-Bernard difference equation (qKZB) with step p and values in a tensor product of finite dimensional evaluation modules over the elliptic quantum…
E. Mukhin, A. VarchenkoDec 26, 1997
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Eigenfunctions of Macdonald's q-difference operator for the root system of type Cn
We construct an integral representation of eigenfunctions for Macdonald's q-difference operator associated with the root system of type Cn . It is given in terms of a restriction of a…
Katsuhisa MimachiDec 25, 1997
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Skew divided difference operators and Schubert polynomials
We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted…
Anatol N. KirillovDec 25, 1997
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A characterization of interpolation Macdonald polynomials
In this elementary paper we prove that the extra vanishing property characterizes the BC interpolation Macdonald polynomials inside a very general class of multivariate interpolation polynomials. It…
Andrei OkounkovDec 23, 1997
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On Cherednik-Macdonald-Mehta identities
In this note we give a short proof of Cherednik's generalization of Macdonald-Mehta identities for the root system An-1 using the representation theory of quantum groups. These identities,…
Pavel Etingof, Alexander KirillovDec 23, 1997
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Centralizer construction for twisted Yangians
For each of the classical Lie algebras g(n)=o(2n+1), sp(2n), o(2n) of type B, C, D we consider the centralizer of the subalgebra g(n-m) in the universal enveloping algebra U(g(n)). We show that…
Alexander Molev, Grigori OlshanskiDec 22, 1997
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On hypergeometric functions connected with quantum cohomology of flag spaces
Givental's recursion relations for the flag varieties G/B are established.
Vadim SchechtmanDec 20, 1997
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Detecting knot invertibility
We discuss the consequences of the possibility that Vassiliev invariants do not detect knot invertibility as well as the fact that quantum Lie group invariants are known not to do so. On the other…
Greg KuperbergDec 19, 1997
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Non-involutory Hopf algebras and 3-manifold invariants
We present a definition of an invariant #(M,H), defined for every finite-dimensional Hopf algebra (or Hopf superalgebra or Hopf object) H and for every closed, framed 3-manifold M. When H is a…
Greg KuperbergDec 19, 1997
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Finite type invariants, the mapping class group and blinks
The goal of the present paper is to find higher genus surgery formulae for the set of finite-type invariants of homology spheres, and to develop a companion theory of finite-type invariants to be…
Stavros Garoufalidis, Jerome LevineDec 18, 1997
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