234 research outputs found
Chern classes of reductive groups and an adjunction formula
In this paper, I construct noncompact analogs of the Chern classes of
equivariant vector bundles over complex reductive groups. For the tangent
bundle, these Chern classes yield an adjunction formula for the Euler
characteristic of complete intersections in reductive groups. In the case where
the complete intersection is a curve, this formula gives an explicit answer for
the Euler characteristic and the genus of the curve.Comment: LATeX, 26 pages; added references, corrected typo
Gelfand-Zetlin polytopes and flag varieties
I construct a correspondence between the Schubert cycles on the variety of
complete flags in C^n and some faces of the Gelfand-Zetlin polytope associated
with the irreducible representation of SL_n(C) with a strictly dominant highest
weight. The construction is based on a geometric presentation of Schubert cells
by Bernstein-Gelfand-Gelfand using Demazure modules. The correspondence between
the Schubert cycles and faces is then used to interpret the classical Chevalley
formula in Schubert calculus in terms of the Gelfand-Zetlin polytopes. The
whole picture resembles the picture for toric varieties and their polytopes.Comment: 16 pages, 2 figure
Schubert calculus for algebraic cobordism
We establish a Schubert calculus for Bott-Samelson resolutions in the
algebraic cobordism ring of a complete flag variety G/B.Comment: 27 pages, Appendix added, slightly abridged version to appear in
Crell
The Effect of Negators, Modals, and Degree Adverbs on Sentiment Composition
Negators, modals, and degree adverbs can significantly affect the sentiment
of the words they modify. Often, their impact is modeled with simple
heuristics; although, recent work has shown that such heuristics do not capture
the true sentiment of multi-word phrases. We created a dataset of phrases that
include various negators, modals, and degree adverbs, as well as their
combinations. Both the phrases and their constituent content words were
annotated with real-valued scores of sentiment association. Using phrasal terms
in the created dataset, we analyze the impact of individual modifiers and the
average effect of the groups of modifiers on overall sentiment. We find that
the effect of modifiers varies substantially among the members of the same
group. Furthermore, each individual modifier can affect sentiment words in
different ways. Therefore, solutions based on statistical learning seem more
promising than fixed hand-crafted rules on the task of automatic sentiment
prediction.Comment: In Proceedings of the 7th Workshop on Computational Approaches to
Subjectivity, Sentiment and Social Media Analysis (WASSA), San Diego,
California, 201
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