The Experts below are selected from a list of 2157 Experts worldwide ranked by ideXlab platform
Masahiko Miyamoto - One of the best experts on this subject based on the ideXlab platform.
-
regularity of fixed point vertex operator subalgebras
arXiv: Representation Theory, 2016Co-Authors: Scott Carnahan, Masahiko MiyamotoAbstract:We show that if $T$ is a simple non-negatively graded regular vertex operator algebra with a nonsingular Invariant Bilinear Form and $\sigma$ is a finite order automorphism of $T$, then the fixed-point vertex operator subalgebra $T^\sigma$ is also regular. This yields regularity for fixed point vertex operator subalgebras under the action of any finite solvable group. As an application, we obtain an $SL_2(\mathbb{Z})$-compatibility between twisted twining characters for commuting finite order automorphisms of holomorphic vertex operator algebras. This resolves one of the principal claims in the Generalized Moonshine conjecture.
-
a new construction of the moonshine vertex operator algebra over the real number field
Annals of Mathematics, 2004Co-Authors: Masahiko MiyamotoAbstract:We give a new construction of the moonshine module vertex operator algebra V ? , which was originally constructed in [FLM2]. We construct it as a framed VOA over the real number field R. We also offer ways to transForm a structure of framed VOA into another framed VOA. As applications, we study the five framed VOA structures on V Eg and construct many framed VOAs including V ? from a small VOA. One of the advantages of our construction is that we are able to construct V ? as a framed VOA with a positive definite Invariant Bilinear Form and we can easily prove that Aut(V ? ) is the Monster simple group. By similar ways, we also construct an infinite series of holomorphic framed VOAs with finite full automorphism groups. At the end of the paper, we calculate the character of a 3C element of the Monster simple group.
-
a new construction of the moonshine vertex operator algebra over the real number field
arXiv: Quantum Algebra, 1997Co-Authors: Masahiko MiyamotoAbstract:We give a new construction of the moonshine VOA V^{\natural} over the real number field. We proved that V^{\natural} has a positive definite Invariant Bilinear Form and its full automorphism group is the Monster simple group. We also construct an infinite series of meromorphic VOAs whose full automorphism groups are finite. We calculate the trace Form on V^{\natural} for some element of the Monster.
Jonathan Wang - One of the best experts on this subject based on the ideXlab platform.
-
on an Invariant Bilinear Form on the space of automorphic Forms via asymptotics
Duke Mathematical Journal, 2018Co-Authors: Jonathan WangAbstract:This article concerns the study of a new Invariant Bilinear Form $\mathcal B$ on the space of automorphic Forms of a split reductive group $G$ over a function field. We define $\mathcal B$ using the asymptotics maps from Bezrukavnikov-Kazhdan and Sakellaridis-Venkatesh, which involve the geometry of the wonderful compactification of $G$. We show that $\mathcal B$ is naturally related to miraculous duality in the geometric Langlands program through the functions-sheaves dictionary. In the proof, we highlight the connection between the classical non-Archimedean Gindikin-Karpelevich Formula and certain factorization algebras acting on geometric Eisenstein series. We then give another definition of $\mathcal B$ using the constant term operator and the inverse of the standard intertwining operator. The Form $\mathcal B$ defines an invertible operator $L$ from the space of compactly supported automorphic Forms to a new space of "pseudo-compactly" supported automorphic Forms. We give a Formula for $L^{-1}$ in terms of pseudo-Eisenstein series and constant term operators which suggests that $L^{-1}$ is an analog of the Aubert-Zelevinsky involution.
-
on an Invariant Bilinear Form on the space of automorphic Forms via asymptotics
Duke Mathematical Journal, 2018Co-Authors: Jonathan WangAbstract:This article concerns the study of a new Invariant Bilinear Form B on the space of automorphic Forms of a split reductive group G over a function field. We define B using the asymptotics maps from recent work of Bezrukavnikov, Kazhdan, Sakellaridis, and Venkatesh, which involve the geometry of the wonderful compactification of G. We show that B is naturally related to miraculous duality in the geometric Langlands program through the functions-sheaves dictionary. In the proof, we highlight the connection between the classical non-Archimedean Gindikin–Karpelevich Formula and certain factorization algebras acting on geometric Eisenstein series. We then give another definition of B using the constant term operator and the inverse of the standard intertwining operator. The Form B defines an invertible operator L from the space of compactly supported automorphic Forms to a new space of pseudocompactly supported automorphic Forms. We give a Formula for L−1 in terms of pseudo-Eisenstein series and constant term operators which suggests that L−1 is an analogue of the Aubert–Zelevinsky involution.
-
on a strange Invariant Bilinear Form on the space of automorphic Forms
Selecta Mathematica-new Series, 2016Co-Authors: Vladimir Drinfeld, Jonathan WangAbstract:Let F be a global field and \(G:=SL(2)\). We study the Bilinear Form \({{\mathcal {B}}}\) on the space of K-finite smooth compactly supported functions on \(G({\mathbb {A}})/G(F)\) defined by $$\begin{aligned} {{\mathcal {B}}}(f_1,f_2):={{\mathcal {B}}}_{\mathrm {naive}}(f_1,f_2)-\langle M^{-1}{{\mathrm{{CT}}}}(f_1)\, ,{{\mathrm{{CT}}}}(f_2)\rangle , \end{aligned}$$ where \({{\mathcal {B}}}_{\mathrm {naive}}\) is the usual scalar product, \({{\mathrm{{CT}}}}\) is the constant term operator, and M is the standard intertwiner. This Form is natural from the viewpoint of the geometric Langlands program. To justify this claim, we provide a dictionary between the classical and ‘geometric’ theory of automorphic Forms. We also show that the Form \({{\mathcal {B}}}\) is related to S. Schieder’s Picard–Lefschetz oscillators.
-
on a strange Invariant Bilinear Form on the space of automorphic Forms
arXiv: Number Theory, 2015Co-Authors: Vladimir Drinfeld, Jonathan WangAbstract:Let F be a global field and A its ring of adeles. Let G:=SL(2). We study the Bilinear Form B on the space of K-finite smooth compactly supported functions on G(A )/G(F) defined by the Formula B (f,g):=B'(f,g)-(M^{-1}CT (f),CT (g)), where B' is the usual scalar product, CT is the constant term operator, and M is the standard intertwiner. This Form is natural from the viewpoint of the geometric Langlands program. To justify this claim, we provide a dictionary between the classical and "geometric" theory of automorphic Forms. We also show that the Form B is related to S. Schieder's Picard-Lefschetz oscillators.
Miyamoto Masahiko - One of the best experts on this subject based on the ideXlab platform.
-
$C_2$-cofiniteness of orbifold models for finite groups
2019Co-Authors: Miyamoto MasahikoAbstract:We prove that if $V$ is a $C_2$-cofinite simple vertex operator algebra of CFT-type with a nonsingular Invariant Bilinear Form and its an automorphism group $G$ is finite, then an orbifold model $V^G$ is also $C_2$-cofinite.Comment: There is a serious gap in this pape
-
Regularity of fixed-point vertex operator subalgebras
2018Co-Authors: Carnahan Scott, Miyamoto MasahikoAbstract:We show that if $T$ is a simple non-negatively graded regular vertex operator algebra with a nonsingular Invariant Bilinear Form and $\sigma$ is a finite order automorphism of $T$, then the fixed-point vertex operator subalgebra $T^\sigma$ is also regular. This yields regularity for fixed point vertex operator subalgebras under the action of any finite solvable group. As an application, we obtain an $SL_2(\mathbb{Z})$-compatibility between twisted twining characters for commuting finite order automorphisms of holomorphic vertex operator algebras. This resolves one of the principal claims in the Generalized Moonshine conjecture.Comment: (v4) additional explanations; 41 page
Skvortsov Evgeny - One of the best experts on this subject based on the ideXlab platform.
-
On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
'American Physical Society (APS)', 2020Co-Authors: Grigoriev Maxim, Mkrtchyan Karapet, Skvortsov EvgenyAbstract:We study the problem of interacting theories with (partially)-massless and conFormal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends the well-known class of purely massless theories. More generally, it is proved that the complete theory has to have a Form of the flatness condition for a connection of a Lie algebra, which, provided there is a non-degenerate Invariant Bilinear Form, can be derived from the Chern-Simons action. We also point out the existence of higher spin theories without the dynamical graviton in the spectrum. As an application of a more general statement that the frame-like Formulation can be systematically constructed starting from the metric one by employing a combination of the local BRST cohomology technique and the parent Formulation approach, we also obtain an explicit uplift of any given metric-like vertex to its frame-like counterpart. This procedure is valid for general gauge theories while in the case of higher spin fields in d-dimensional Minkowski space one can even use as a starting point metric-like vertices in the transverse-traceless gauge. In particular, this gives the fully off-shell lift for transverse-traceless vertices.Comment: 35 pages+Appendice
Skvortsov E. - One of the best experts on this subject based on the ideXlab platform.
-
Matter-free higher spin gravities in 3D: Partially-massless fields and general structure
'American Physical Society (APS)', 2020Co-Authors: Grigoriev M., Mkrtchyan K., Skvortsov E.Abstract:We study the problem of interacting theories with (partially)-massless and conFormal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends the well-known class of purely massless theories. More generally, it is proved that the complete theory has to have a Form of the flatness condition for a connection of a Lie algebra, which, provided there is a non-degenerate Invariant Bilinear Form, can be derived from the Chern-Simons action. We also point out the existence of higher spin theories without the dynamical graviton in the spectrum. As an application of a more general statement that the frame-like Formulation can be systematically constructed starting from the metric one by employing a combination of the local BRST cohomology technique and the parent Formulation approach, we also obtain an explicit uplift of any given metric-like vertex to its frame-like counterpart. This procedure is valid for general gauge theories while in the case of higher spin fields in d-dimensional Minkowski space one can even use as a starting point metric-like vertices in the transverse-traceless gauge. In particular, this gives the fully off-shell lift for transverse-traceless vertices
