#### Alladi Ramakrishnan Hall

#### Rank-level duality of Conformal Blocks

#### Swarnava Mukhopadhyay

##### University of Maryland

*Classical invariants for representations of one Lie group can*

often be related to invariants of some other Lie group. Physics suggests

that the right objects to consider for these questions are certain

refinements of classical invariants known as conformal blocks. Conformal

blocks appear in algebraic geometry as spaces of global sections of line

bundles on the moduli stack of parabolic bundles on a smooth curve.

Rank-level duality connects a conformal block associated to one Lie algebra

to a conformal block for a different Lie algebra.

In this talk, we will first discuss rank-level duality for the pair

orthogonal and spin groups on the projective line and then for the pair

(G_2, F_4) over a smooth curve of genus g. If time permits, we will discuss

rank-level duality for odd orthogonal groups over curves of positive genus.

The later is joint with Richard Wentworth.

Done