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S. Kolb

Publications and source records attributed to S. Kolb.

11 recordsLinked to original sources
arXiv2011

Homogeneous right coideal subalgebras of quantized enveloping algebras

For a quantized enveloping algebra of a complex semisimple Lie algebra with deformation parameter not a root of unity, we classify all homogeneous right coideal subalgebras. Any such right coideal subalgebra is determined uniquely by a triple consisting of two elements of the Weyl group and a subset of the set of simple roots satisfying some natural conditions. The essential ingredients of the proof are the Lusztig automorphisms and the classification of homogeneous right coideal subalgebras of the Borel Hopf subalgebras of quantized enveloping algebras obtained previously by H.-J. Schneider and the first named author. Key words: Quantum groups, coideal subalgebras, Weyl group, weak order

math.QA↗
arXiv2009

Right coideal subalgebras of the Borel part of a quantized enveloping algebra

For the Borel part of a quantized enveloping algebra we classify all right coideal subalgebras for which the intersection with the coradical is a Hopf algebra. The result is expressed in terms of characters of the subalgebras $U^+[w]$ of the quantized enveloping algebra, introduced by de Concini, Kac, and Procesi for any Weyl group element $w$. We explicitly determine all characters of $U^+[w]$ building on recent work by Yakimov on prime ideals of $U^+[w]$ which are invariant under a torus action. Key words: Quantum groups, coideal subalgebras

math.QA↗
arXiv2006

On the Bernstein-Gelfand-Gelfand resolution for Kac-Moody algebras and quantized enveloping algebras

A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-Gelfand resolution for symmetrizable Kac-Moody algebras are established. For quantized enveloping algebras with fixed complex nonzero deformation parameter q exactness is proven for all q which are not a root of unity.

math.QA↗
arXiv2006

The center of quantum symmetric pair coideal subalgebras

The theory of quantum symmetric pairs as developed by the second author is based on coideal subalgebras of the quantized universal enveloping algebra for a semisimple Lie algebra. This paper investigates the center of these coideal subalgebras, proving that the center is a polynomial ring. A basis of the center is given in terms of a submonoid of the dominant integral weights.

math.QA↗
arXiv2003

De Rham Complex for Quantized Irreducible Flag Manifolds

It is shown that quantized irreducible flag manifolds possess a canonical $q$-analogue of the de Rham complex. Generalizing the well known situation for the standard Podleś' quantum sphere this analogue is obtained as the universal differential calculus of a distinguished first order differential calculus. The corresponding differential $\dif$ can be written as a sum of differentials $\del$ and $\delbar$. The universal differential calculus corresponding to the first order differential calculi $\dif$, $\del$, and $\delbar$ are given in terms of generators and relations. Relations to well known quantized exterior algebras are established. The dimensions of the homogeneous components are shown to be the same as in the classical case. The existence of a volume form is proven.

math.QA↗
arXiv2003

The Locally Finite Part of the Dual Coalgebra of Quantized Irreducible Flag Manifolds

The notion of locally finite part of the dual coalgebra of certain quantized coordinate rings is introduced. In the case of irreducible flag manifolds this locally finite part is shown to coincide with a natural quotient coalgebra V of U_q(g). On the way the coradical filtration of V is determined. A graded version of the duality between V and the quantized coordinate ring is established. This leads to a natural construction of several examples of quantized vector spaces. As an application covariant first order differential calculi on quantized irreducible flag manifolds are classified. Keywords: quantum groups, quantized flag manifolds

math.QA↗
arXiv2001

Differential Calculus on Quantum Complex Grassmann Manifolds II: Classification

For differential calculi over certain right coideal subalgebras of quantum groups the notion of quantum tangent space is introduced. In generalization of a result by Woronowicz a one to one correspondence between quantum tangent spaces and covariant first order differential calculi is established. This result is used to classify differential calculi over quantum Grassmann manifolds. It turns out that up to special cases in low dimensions there exists exactly one such calculus of classical dimension 2r(N-r). Keywords: Quantum groups, quantum spaces, quantum Grassmann manifolds, differential calculus

math.QA↗
arXiv2001

Latest Results from the Heidelberg-Moscow Double Beta Decay Experiment

New results for the double beta decay of 76Ge are presented. They are extracted from Data obtained with the HEIDELBERG-MOSCOW, which operates five enriched 76Ge detectors in an extreme low-level environment in the GRAN SASSO. The two neutrino accompanied double beta decay is evaluated for the first time for all five detectors with a statistical significance of 47.7 kg y resulting in a half life of (T_(1/2))^(2nu) = [1.55 +- 0.01 (stat) (+0.19) (-0.15) (syst)] x 10^(21) years. The lower limit on the half-life of the 0nu beta-beta decay obtained with pulse shape analysis is (T_(1/2))^(0_nu) > 1.9 x 10^(25) [3.1 x 10^(25)] years with 90% C.L. (68% C.L.) (with 35.5 kg y). This results in an upper limit of the effective Majorana neutrino mass of 0.35 eV (0.27 eV). No evidence for a Majoron emitting decay mode or for the neutrinoless mode is observed.

hep-ph↗
arXiv1998

New limits on dark--matter WIMPs from the Heidelberg--Moscow experiment

New results after 0.69 kg yr of measurement with an enriched 76Ge detector of the Heidelberg--Moscow experiment with an active mass of 2.758 kg are presented. An energy threshold of 9 keV and a background level of 0.042 counts/(kg d keV) in the energy region between 15 keV and 40 keV was reached.The derived limits on the WIMP--nucleon cross section are the most stringent limits on spin--independent interactions obtained to date by using essentially raw data without background subtraction.

hep-ex↗