435 research outputs found
On dynamical r-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras
According to Etingof and Varchenko, the classical dynamical Yang-Baxter
equation is a guarantee for the consistency of the Poisson bracket on certain
Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these
Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair
\L\subset \A to those on another pair \K\subset \A, where \K\subset
\L\subset \A is a chain of Lie algebras for which \L admits a reductive
decomposition as \L=\K+\M. Several known dynamical r-matrices appear
naturally in this setting, and its application provides new r-matrices, too. In
particular, we exhibit a family of r-matrices for which the dynamical variable
lies in the grade zero subalgebra of an extended affine Lie algebra obtained
from a twisted loop algebra based on an arbitrary finite dimensional self-dual
Lie algebra.Comment: 19 pages, LaTeX, added a reference and a footnote and removed some
typo
Halving spaces and lower bounds in real enumerative geometry
We develop the theory of halving spaces to obtain lower bounds in real
enumerative geometry. Halving spaces are topological spaces with an action of a
Lie group with additional cohomological properties. For
we recover the conjugation spaces of Hausmann, Holm and
Puppe. For we obtain the circle spaces. We show that
real even and quaternionic partial flag manifolds are circle spaces leading to
non-trivial lower bounds for even real and quaternionic Schubert problems. To
prove that a given space is a halving space, we generalize results of Borel and
Haefliger on the cohomology classes of real subvarieties and their
complexifications. The novelty is that we are able to obtain results in
rational cohomology instead of modulo 2. The equivariant extension of the
theory of circle spaces leads to generalizations of the results of Borel and
Haefliger on Thom polynomials.Comment: 30 page
W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)
We show that that the Jacobi-identities for a W-algebra with primary fields
of dimensions 3, 4 and 5 allow two different solutions. The first solution can
be identified with WA_4. The second is special in the sense that, even though
associative for general value of the central charge, null-fields appear that
violate some of the Jacobi-identities, a fact that is usually linked to
exceptional W-algebras. In contrast we find for the algebra that has an
additional spin 6 field only the solution WA_5.Comment: 17 pages, LaTeX, KCL-TH-92-9, DFFT-70/9
Evaluation of an online fermentation monitoring system
The need to introduce promising bioethanol production technologies calls for advanced laboratory techniques to study experiment designs and to obtain their results in a quick and reliable way. Real time monitoring based on general principles of ethanol fermentation, such as effluent CO2 volume, avoids time consuming steps, long lasting analyses and delivers information about the process directly. A device based on the above features and capable for real time monitoring on parallel channels was developed by the authors and is described in this paper. Both for calibration and for fermentation, test runs were carried out on different days and channels. Statistical evaluation was based on the obtained data. According to the t-test (P=0.05) and Grubbs analysis, the calibration method is reliable regardless of the date of calibration. When evaluating the fermentation results by ANCOVA acceptable standard derivations were obtained as impact of channel (58.8 ml), date (82.1 ml) and incorporating all impacts (116.2 ml). The final ethanol concentrations calculated based on the gas volume were compared to ones determined by HPLC and an average difference of 10% was found. Thus, the device proved to be advantageous in monitoring fermentation
On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions
We clarify the notion of the DS --- generalized Drinfeld-Sokolov ---
reduction approach to classical -algebras. We first strengthen an
earlier theorem which showed that an embedding can be associated to every DS reduction. We then use the fact that a
\W-algebra must have a quasi-primary basis to derive severe restrictions on
the possible reductions corresponding to a given embedding. In the
known DS reductions found to date, for which the \W-algebras are denoted by
-algebras and are called canonical, the
quasi-primary basis corresponds to the highest weights of the . Here we
find some examples of noncanonical DS reductions leading to \W-algebras which
are direct products of -algebras and `free field'
algebras with conformal weights . We also show
that if the conformal weights of the generators of a -algebra
obtained from DS reduction are nonnegative (which isComment: 48 pages, plain TeX, BONN-HE-93-14, DIAS-STP-93-0
Unifying W-Algebras
We show that quantum Casimir W-algebras truncate at degenerate values of the
central charge c to a smaller algebra if the rank is high enough: Choosing a
suitable parametrization of the central charge in terms of the rank of the
underlying simple Lie algebra, the field content does not change with the rank
of the Casimir algebra any more. This leads to identifications between the
Casimir algebras themselves but also gives rise to new, `unifying' W-algebras.
For example, the kth unitary minimal model of WA_n has a unifying W-algebra of
type W(2,3,...,k^2 + 3 k + 1). These unifying W-algebras are non-freely
generated on the quantum level and belong to a recently discovered class of
W-algebras with infinitely, non-freely generated classical counterparts. Some
of the identifications are indicated by level-rank-duality leading to a coset
realization of these unifying W-algebras. Other unifying W-algebras are new,
including e.g. algebras of type WD_{-n}. We point out that all unifying quantum
W-algebras are finitely, but non-freely generated.Comment: 13 pages (plain TeX); BONN-TH-94-01, DFTT-15/9
A note on the Gauss decomposition of the elliptic Cauchy matrix
Explicit formulas for the Gauss decomposition of elliptic Cauchy type
matrices are derived in a very simple way. The elliptic Cauchy identity is an
immediate corollary.Comment: 5 page
On the scattering theory of the classical hyperbolic C(n) Sutherland model
In this paper we study the scattering theory of the classical hyperbolic
Sutherland model associated with the C(n) root system. We prove that for any
values of the coupling constants the scattering map has a factorized form. As a
byproduct of our analysis, we propose a Lax matrix for the rational C(n)
Ruijsenaars-Schneider-van Diejen model with two independent coupling constants,
thereby setting the stage to establish the duality between the hyperbolic C(n)
Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.Comment: 15 page
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