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We provide an explicit integral representation for L-functions of pairs (F,g) where F is a holomorphic genus 2 Siegel newform and g a holomorphic elliptic newform, both of squarefree levels and of equal weights. When F,g have level one,…

Number Theory · Mathematics 2009-01-17 Abhishek Saha

Let K be the kernel of an epimorphism G -> Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3, or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group…

Geometric Topology · Mathematics 2007-05-23 Daniel S. Silver , Susan G. Williams

We present an integral representation for the tensor product $L$-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical…

Number Theory · Mathematics 2018-08-03 Yuanqing Cai , Solomon Friedberg , David Ginzburg , Eyal Kaplan

We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2), su(3), and g(2). This leads to an efficient practical method to reduce tensor…

Mathematical Physics · Physics 2016-06-22 N. D. Vlasii , F. von Rütte , U. -J. Wiese

For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a "universal" hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in…

Dynamical Systems · Mathematics 2014-09-19 Eli Glasner , Benjamin Weiss

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite…

Representation Theory · Mathematics 2016-05-03 Mahmood Alaghmandan , Massoud Amini

Let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group \Gamma generated by r elements, we consider the representation spaces Hom(\Gamma,G) and Hom(\Gamma,K) with the natural…

Group Theory · Mathematics 2015-06-03 Maxime Bergeron

A representation of the Quantum Toroidal Algebra of type sl(N) is constructed on every irreducible integrable highest weight module of the Quantum Affine Algebra of type gl(N). As an intermediate step in the construction, we obtain a…

Quantum Algebra · Mathematics 2007-05-23 K. Takemura , D. Uglov

We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is the group algebra of a group $G$, the invariant counts homomorphisms from the fundamental group of the manifold to $G$. The…

Quantum Algebra · Mathematics 2016-09-06 Greg Kuperberg

In this article, we establish an asymptotic lower bound estimate on the contribution of cuspidal automorphic representations of ${\rm GL}_4(\mathbb A_{\mathbb Q})$ to cuspidal cohomology of the ${\rm GL}_4$ which are obtained from…

Number Theory · Mathematics 2021-11-11 Chandrasheel Bhagwat , Sudipa Mondal

For each valued quiver $Q$ of Dynkin type, we construct a valued ice quiver $\Delta_Q^2$. Let $G$ be a simple connected Lie group with Dynkin diagram the underlying valued graph of $Q$. The upper cluster algebra of $\Delta_Q^2$ is graded by…

Representation Theory · Mathematics 2021-12-01 Jiarui Fei

We find experimental examples of congruences of Hecke eigenvalues between automorphic representations of groups such as $\mathrm{GSp}_2(\mathbb{A})$, $\mathrm{SO}(4,3)(\mathbb{\mathbb{A}})$ and $\mathrm{SO}(5,4)(\mathbb{A})$, where the…

Number Theory · Mathematics 2020-03-20 Jonas Bergström , Neil Dummigan , David Farmer , Sally Koutsoliotas

Let $G$ be a classical complex Lie group, $P$ any parabolic subgroup of $G$, and $G/P$ the corresponding partial flag variety. We prove an explicit combinatorial Giambelli formula which expresses an arbitrary Schubert class in the…

Algebraic Geometry · Mathematics 2014-04-01 Harry Tamvakis

We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with…

Operator Algebras · Mathematics 2007-05-23 Erik Bedos , Roberto Conti

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…

High Energy Physics - Theory · Physics 2009-10-30 M. R. Gaberdiel

We introduce a notion of $R$-quadratic maps between modules over a commutative ring $R$ which generalizes several classical notions arising in linear algebra and group theory. On a given module $M$ such maps are represented by $R$-linear…

Commutative Algebra · Mathematics 2011-07-12 H. Gaudier , M. Hartl

We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary…

Number Theory · Mathematics 2018-03-23 Ameya Pitale , Abhishek Saha , Ralf Schmidt

For the second fundamental representation of the general linear group over a commutative ring $R$ we construct straightforward and uniform polynomial expressions of elementary generators as products of elementary conjugates of an arbitrary…

Group Theory · Mathematics 2024-05-31 Roman Lubkov

In the previous paper, we proposed a practical method of constructing explicitly representation groups $R(G)$ for finite groups $G$, and apply it to certain typical finite groups $G$ with Schur multiplier $M(G)$ containing prime number 3.…

Representation Theory · Mathematics 2024-08-30 Tatsuya Tsurii , Satoe Yamanaka , Itsumi Mikami , Takeshi Hirai

We give an explicit formula for the twisted gamma factor for a pair of irreducible supercuspidal representations of level zero. We also obtain an explicit formula for the unramified base change of level zero supercuspidal representations.

Representation Theory · Mathematics 2019-03-28 Chang Yang
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