Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2508.07109

Representations of conformal nets associated with infinite-dimensional groups

Maria Stella Adamo·Luca Giorgetti·Yoh Tanimoto
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the relation between representations of certain infinite-dimensional Lie groups and those of the associated conformal nets. For a chiral conformal net extending the net generated by the vacuum representation of a loop group or diffeomorphism group of the circle, we show that any conformal net representation induces a positive-energy representation of the corresponding group. Consequently, we prove that any representation of such a conformal net is automatically diffeomorphism covariant. Moreover, we show that the covariance cocycles of conformal net representations satisfy naturality with respect to the action of diffeomorphisms, i.e. the diffeomorphisms act equivariantly on the category of conformal net representations.

Explore related subjects

math.RTmath-phmath.MPmath.OA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Maria Stella Adamo, Luca Giorgetti, Yoh Tanimoto. 2025-08-09. Representations of conformal nets associated with infinite-dimensional groups. https://arxiv.org/abs/2508.07109

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Course on Lie algebras and Chevalley groups

These are expanded notes from graduate courses about Lie algebras and Chevalley groups held at the University of Stuttgart. In the 1950s Chevalley showed how linear groups over arbitrary fields could be obtained~ -- ~by a uniform procedure~ -- ~from the simple Lie algebras over $\C$ occurring in the Cartan--Killing classification. Together with subsequent variations, Chevalley's work had a profound and long-lasting impact on group theory and Lie theory in general. Classical, and widely used references are the lectures notes by Steinberg (1967) and the monograph by Carter (1972). Our aim here is to present a self-contained introduction to the theory of Chevalley groups, based on recent simplifications arising from Lusztig's fundamental theory of ``canonical bases''. A further feature of our text is that we explicitly incorporate algorithmic methods in our treatment, both for the handling of substantial examples and regarding some aspects of the general theory. Eventually, this may turn into a book project.

math.RT↗
arXiv2026

On the p-part of the conductor of a generalised character

We show that the $p$-part of the conductor of a generalised character of a finite group is equal to the conductor of its generalised decomposition numbers. We use this to show that $p$-parts of conductors of irreducible characters are preserved under isotypies and perfect isometries that arise in the context of stable equivalences of Morita type with endopermutation source. We apply this to blocks with abelian defect and Frobenius inertial quotient.

math.RT↗
arXiv2026

On the triviality of inhomogeneous deformations of $\mathfrak{osp}(1|2n)$

We specify a symmetrized mixed-oscillator deformation family of $B(0,n)=\operatorname{osp}(1|2n)$, with even mixed coefficients and one odd square-zero parameter. For every $n\geq1$, we derive its bracket from a faithful oscillator realization and exhibit an odd cochain whose coboundary is the recovered deformation coefficient. The resulting even change of generators is an exact isomorphism over the exterior parameter algebra. For $n=1$, the cochain agrees with the normalization of Bakalov-Sullivan. We give the source relations and the even-central specialization explicitly, together with a Lean 4 formalization.

math.RT↗