Biomedical subjects

Victor Guillemin

Publications and source records attributed to Victor Guillemin.

2 recordsLinked to original sources

PubMed2004

Signature quantization and representations of compact Lie groups.

We discuss some applications of signature quantization to the representation theory of compact Lie groups. In particular, we prove signature analogues of the Kostant formula for weight multiplicities and the Steinberg formula for tensor product multiplicities. Using symmetric functions, we also find, for type A, analogues of the Weyl branching rule and the Gel'fand-Tsetlin theorem.

Journal Article↗

PubMed2003

Signature quantization.

We associate to the action of a compact Lie group G on a line bundle over a compact oriented even-dimensional manifold a virtual representation of G using a twisted version of the signature operator. We obtain analogues of various theorems in the more standard theory of geometric quantization.

Journal Article↗