Chern–Simons forms and higher character maps of Lie representations
Y Berest, G Felder, S Patotski… - International …, 2016 - academic.oup.com
International Mathematics Research Notices, 2016•academic.oup.com
We study the derived representation scheme DRep g (a) parameterizing the representations
of a Lie algebra a in a reductive Lie algebra g. In our earlier work, we defined two canonical
maps Tr g (a): HC•(r)(a)→ H•[DRep g (a)] G and Φ g (a): H•[DRep g (a)] G→ H•[DRep h (a)]
W, called the Drinfeld trace and the derived Harish-Chandra homomorphism, respectively. In
this paper, we give general formulas for these maps in terms of Chern–Simons forms. As a
consequence, we show that, if a is an abelian Lie algebra, the composite map Φ g (a)° Tr g …
of a Lie algebra a in a reductive Lie algebra g. In our earlier work, we defined two canonical
maps Tr g (a): HC•(r)(a)→ H•[DRep g (a)] G and Φ g (a): H•[DRep g (a)] G→ H•[DRep h (a)]
W, called the Drinfeld trace and the derived Harish-Chandra homomorphism, respectively. In
this paper, we give general formulas for these maps in terms of Chern–Simons forms. As a
consequence, we show that, if a is an abelian Lie algebra, the composite map Φ g (a)° Tr g …
We study the derived representation scheme parameterizing the representations of a Lie algebra in a reductive Lie algebra . In our earlier work , we defined two canonical maps and Φg(a): H•[DRepg(a)]G→H•[DReph(a)]W, called the Drinfeld trace and the derived Harish-Chandra homomorphism, respectively. In this paper, we give general formulas for these maps in terms of Chern–Simons forms. As a consequence, we show that, if is an abelian Lie algebra, the composite map is given by a canonical differential operator defined on differential forms on and depending only on the Cartan data , where . We derive a combinatorial formula for this operator that plays a key role in the study of derived commuting schemes in .
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