354,010 research outputs found
Toward parton equilibration with improved parton interaction matrix elements
The Quark-Gluon Plasma can be produced in high energy heavy ion collisions
and how it equilibrates is important for the extraction of the properties of
strongly interacting matter. A radiative transport model can be used to reveal
interesting characteristics of Quark-Gluon Plasma thermalization. For example,
screened parton interactions always lead to partial pressure isotropization.
Systems with different initial pressure anisotropies evolve toward the same
asymptotic evolution. In particular, radiative processes are crucial for the
chemical equilibration of the system. Matrix elements under the soft and
collinear approximation for these processes, as first derived by Gunion and
Bertsch, are widely used. A different approach is to start with the exact
matrix elements for the two to three and its inverse processes. General
features of this approach will be reviewed and the results will be compared
with the Gunion-Bertsch results. We will comment on the possible implications
of the exact matrix element approach on Quark-Gluon Plasma thermalization.Comment: Presented at the 11th International Conference on Nucleus-Nucleus
Collisions (NN2012), San Antonio, Texas, USA, 27 May-1 June 201
Dual canonical bases for the quantum general linear supergroup
Dual canonical bases of the quantum general linear supergroup are constructed
which are invariant under the multiplication of the quantum Berezinian. By
setting the quantum Berezinian to identity, we obtain dual canonical bases of
the quantum special linear supergroup {\s O}_q(SL_{m\mid n}). We apply the
canonical bases to study invariant subalgebras of the quantum supergroups under
left and right translations. In the case , it is shown that each invariant
subalgebra is spanned by a part of the dual canonical bases. This in turn leads
to dual canonical bases for any Kac module constructed by using an analogue of
Borel-Weil theorem.Comment: 32 page
Quantum superalgebra representations on cohomology groups of non-commutative bundles
Quantum homogeneous supervector bundles arising from the quantum general
linear supergoup are studied. The space of holomorphic sections is promoted to
a left exact covariant functor from a category of modules over a quantum
parabolic sub-supergroup to the category of locally finite modules of the
quantum general linear supergroup. The right derived functors of this functor
provides a form of Dolbeault cohomology for quantum homogeneous supervector
bundles. We explicitly compute the cohomology groups, which are given in terms
of well understood modules over the quantized universal enveloping algebra of
the general linear superalgebra.Comment: 24 page
Quantum supergroups and topological invariants of three - manifolds
The Reshetikhin - Turaeve approach to topological invariants of three -
manifolds is generalized to quantum supergroups. A general method for
constructing three - manifold invariants is developed, which requires only the
study of the eigenvalues of certain central elements of the quantum supergroup
in irreducible representations. To illustrate how the method works,
at odd roots of unity is studied in detail, and the
corresponding topological invariants are obtained.Comment: 22 page
Topological Invariants For Lens Spaces And Exceptional Quantum Groups
The Reshetikhin - Turaev invariants arising from the quantum groups
associated with the exceptional Lie algebras , and at odd
roots of unity are constructed and explicitly computed for all the lens spaces.Comment: LaTeX 10 page
Serre presentations of Lie superalgebras
An analogue of Serre's theorem is established for finite dimensional simple
Lie superalgebras, which describes presentations in terms of Chevalley
generators and Serre type relations relative to all possible choices of Borel
subalgebras. The proof of the theorem is conceptually transparent; it also
provides an alternative approach to Serre's theorem for ordinary Lie algebras.Comment: 45 page
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