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A level-one representation of the quantum affine superalgebra \U_q(\hat{\frak{sl}}(M+1|N+1))
A level-one representation of the quantum affine superalgebra
\U_q(\hat{\frak{sl}}(M+1|N+1)) and vertex operators associated with the
fundamental representations are constructed in terms of free bosonic fields.
Character formulas of level-one irreducible highest weight modules of
\U_q(\hat{\frak{sl}}(2|1)) are conjectured.Comment: AMS-TeX, 11 page
Chern Classes and Compatible Power Operations in Inertial K-theory
Let [X/G] be a smooth Deligne-Mumford quotient stack. In a previous paper the
authors constructed a class of exotic products called inertial products on
K(I[X/G]), the Grothendieck group of vector bundles on the inertia stack
I[X/G]. In this paper we develop a theory of Chern classes and compatible power
operations for inertial products. When G is diagonalizable these give rise to
an augmented -ring structure on inertial K-theory.
One well-known inertial product is the virtual product. Our results show that
for toric Deligne-Mumford stacks there is a -ring structure on
inertial K-theory. As an example, we compute the -ring structure on
the virtual K-theory of the weighted projective lines P(1,2) and P(1,3). We
prove that after tensoring with C, the augmentation completion of this
-ring is isomorphic as a -ring to the classical K-theory of
the crepant resolutions of singularities of the coarse moduli spaces of the
cotangent bundles and , respectively. We interpret this
as a manifestation of mirror symmetry in the spirit of the Hyper-Kaehler
Resolution Conjecture.Comment: Many improvements. Special thanks to the referee for helpful
suggestions. To appear in Annals of K-Theory. arXiv admin note: text overlap
with arXiv:1202.060
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