Kavli Affiliate: Mikhail Kapranov
| First 5 Authors: Mikhail Kapranov, Vadim Schechtman, , ,
| Summary:
We consider the space Z(C,L) of 0-cycles on the complex line C with
coefficients in a commutative monoid L subject to certain conditions. Such
spaces include the symmetric products (for L=Z_+) and the Ran space (for L=T={
True, False} being the Boolean algebra of truth values). We describe the
appropriately defined category of perverse sheaves on Z(C,L) in terms of the
braided category (PROB) generated by the components of the universal $L$-graded
bialgebra. We give another description in terms of so-called Janus sheaves
which are objects of mixed functoriality (data covariant in one direction and
contravariant in the other) on a category formed by certain matrices with
entries in L. The matrices in question are analogs of contingency tables
familiar in statistics.
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