Publication details

Equivariant quantizations for AHS-structures


ŠILHAN Josef ČAP Andreas

Year of publication 2010
Type Article in Periodical
Magazine / Source Advances in Mathematics
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords equivariant quantization; natural quantization; parabolic geometry; AHS--structure; tractor calculus
Description We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so--called AHS--structure. Outside of a finite set of critical (or resonant) weights, this procedure gives rise to a quantization, which is intrinsic to this geometric structure. In particular, this provides projectively and conformally equivariant quantizations for arbitrary symbols on general (curved) projective and conformal structures.
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