Paolo Papi
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View article: Spectral flow and application to unitarity of representations of minimal $W$-algebras
Spectral flow and application to unitarity of representations of minimal $W$-algebras Open
Using spectral flow, we provide a proof of [9, Theorem 9.17] on unitarity of Ramond twisted non-extremal representations of minimal $W$-algebras that does not rely on the still conjectural exactness of the twisted quantum reduction functor…
View article: Extremal unitary representations of big $N=4$ superconformal algebra
Extremal unitary representations of big $N=4$ superconformal algebra Open
In this paper we give a detailed proof of the classification of extremal (=massless) unitary highest weight representations in the Neveu Schwarz and Ramond sectors of the big $N=4$ superconformal algebra which can be found in [5]. Our resu…
View article: On the Intersection Problem for Quantum Finite Automata
On the Intersection Problem for Quantum Finite Automata Open
This paper is a continuation of a previous study on the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We investigate conditions assuring that, given a language recognized by such a device…
View article: Unitarity of minimal $W$-algebras and their representations II: Ramond sector
Unitarity of minimal $W$-algebras and their representations II: Ramond sector Open
In this paper we study unitary Ramond twisted representations of minimal $W$-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as wel…
View article: Defining relations for minimal unitary quantum affine W-algebras
Defining relations for minimal unitary quantum affine W-algebras Open
We prove that any unitary highest weight module over a universal minimal quantum affine $W$-algebra at non-critical level descends to its simple quotient. We find the defining relations of the unitary simple minimal quantum affine $W$-alge…
View article: Unitarity of minimal $W$-algebras and their representations I
Unitarity of minimal $W$-algebras and their representations I Open
We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…
View article: New approaches for studying conformal embeddings and collapsing levels for $W$--algebras
New approaches for studying conformal embeddings and collapsing levels for $W$--algebras Open
In this paper we prove a general result saying that under certain hypothesis an embedding of an affine vertex algebra into an affine $W$--algebra is conformal if and only if their central charges coincide. This result extends our previous …
View article: Invariant Hermitian forms on vertex algebras
Invariant Hermitian forms on vertex algebras Open
We study invariant Hermitian forms on a conformal vertex algebra and on their (twisted) modules. We establish existence of a non-zero invariant Hermitian form on an arbitrary [Formula: see text]-algebra. We show that for a minimal simple […
View article: On the semisimplicity of the category $KL_k$ for affine Lie superalgebras
On the semisimplicity of the category $KL_k$ for affine Lie superalgebras Open
We study the semisimplicity of the category $KL_k$ for affine Lie superalgebras and provide a super analog of certain results from arXiv:1801.09880. Let $KL_k^{fin}$ be the subcategory of $KL_k$ consisting of ordinary modules on which the …
View article: Unitarity of minimal $W$-algebras
Unitarity of minimal $W$-algebras Open
We obtain a complete classification of minimal simple unitary $W$-algebras.
View article: Yangians versus minimal W-algebras: A surprising coincidence
Yangians versus minimal W-algebras: A surprising coincidence Open
We prove that the singularities of the [Formula: see text]-matrix [Formula: see text] of the minimal quantization of the adjoint representation of the Yangian [Formula: see text] of a finite dimensional simple Lie algebra [Formula: see tex…
View article: The Bruhat order on abelian ideals of Borel subalgebras
The Bruhat order on abelian ideals of Borel subalgebras Open
Let be a quasi-simple algebraic group over an algebraically closed field whose characteristic is not very bad for , and let be a Borel subgroup of with Lie algebra . Given a -stable abelian subalgebra of the nilradical of , we paramet…
View article: Conformal embeddings in affine vertex superalgebras
Conformal embeddings in affine vertex superalgebras Open
This paper is a natural continuation of our previous work on conformal embeddings of vertex algebras [6], [7], [8]. Here we consider conformal embeddings in simple affine vertex superalgebra Vk(g) where g=g0 ̄⊕g1 ̄ is a basic classical simpl…
View article: Nilpotent orbits of height 2 and involutions in the affine Weyl group
Nilpotent orbits of height 2 and involutions in the affine Weyl group Open
Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B⊂G be a Borel subgroup. Then B acts with finitely many orbits on the variety N2⊂g of the nilpotent elements whos…
View article: Yangians vs minimal W-algebras: a surprizing coincidence
Yangians vs minimal W-algebras: a surprizing coincidence Open
We prove that the singularities of the $R$-matrix $R(k)$ of the minimal quantization of the adjoint representation of the Yangian $Y(\mathfrak g)$ of a finite dimensional simple Lie algebra $\mathfrak g$ are the opposite of the roots of th…
View article: On some modules of covariants for a reflection group
On some modules of covariants for a reflection group Open
Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak h$ and Weyl group $W$. We build up a graded map $(\mathcal H\otimes \bigwedge\mathfrak h\otimes \mathfrak h)^W\to (\bigwedge \mathfrak g\otimes \mathfrak g)^\mathf…
View article: Spherical nilpotent orbits and abelian subalgebras in isotropy representations
Spherical nilpotent orbits and abelian subalgebras in isotropy representations Open
Let G be a simply connected semisimple algebraic group with Lie algebra g, let G(0) subset of G be the symmetric subgroup defined by an algebraic involution sigma and let g(1) subset of g be the isotropy representation of G(0). Given an ab…
View article: Conformal embeddings of affine vertex algebras in minimal $W$-algebras\n II: decompositions
Conformal embeddings of affine vertex algebras in minimal $W$-algebras\n II: decompositions Open
We present methods for computing the explicit decomposition of the minimal\nsimple affine $W$-algebra $W_k(\\mathfrak g, \\theta)$ at a conformal level $k$\nas a module for its maximal affine subalgebra $\\mathcal V_k(\\mathfrak\ng^{\\natu…