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{{Short description|Formula in representation theory}} ...imple complex [[Lie algebra]] in a [[tensor product]] of two [[irreducible representation]]s. ...

{{Short description|Criterion for vector stability in algebraic geometry}} ...riant theory#Stability|stability]] of a vector in a [[group representation|representation]] of a complex [[reductive group]]. If the [[complex number|complex]] [[vec ...

...ion with some problems of [[approximation theory]]. This theorem gives the representation formula for the [[Holomorphic function|holomorphic]] [[Linear subspace|subs }}</ref> contains the following theorem presented also in [[Joseph L. Walsh]]'s well-known monograph ...

...s a closely related theorem classifying the [[Compact group#Representation theory of a connected compact Lie group|irreducible representations]] of a connect ...difference between the two results is in the precise notion of "integral" in the definition of a dominant integral element. If <math>K</math> is simply ...

...tional]]s. The representation has application in finding [[large deviation theory|large deviation]] asymptotics. ...t1=Xicheng|last1=Zhang|publisher=Duke University Press|title=A variational representation for random functionals on abstract Wiener spaces|journal=Journal of Mathema ...

...tation of the symmetric group]] <math>S_n</math> to be zero. It was proven in 1988 by Carlos Gamas.<ref name="Gamas">{{cite journal ...presentation. The tensor <math>v_1 \otimes v_2 \otimes \dots \otimes v_n \in V^{\otimes n}</math> symmetrized by <math>\chi^{\lambda}</math> is defined ...

...is realised in a certain space, of [[square-integrable function]]s, given in a concrete way. ...n]] of a [[Group (mathematics)|group]] ''G'' to a [[subgroup]]&nbsp;''H''. In that context, the pair (''G'',&nbsp;''H'') is called a strong [[Gelfand pai ...

In mathematics, the '''equivariant algebraic K-theory''' is an [[algebraic K-theory]] associated to the category <math>\operatorname{Coh}^G(X)</math> of [[equi ...2–1995)].</ref> Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. ...

In [[abstract algebra]], an '''[[automorphism]] of a [[Lie algebra]]''' <math> ...operatorname{Aut}^0(\mathfrak{g})</math>. These form a [[normal subgroup]] in the group of automorphisms, and the [[quotient group|quotient]] <math>\oper ...

...bout it (reproduced in {{harv|Dedekind|1968}}, with an English translation in {{harv|Curtis|2003|loc=p.&nbsp;51}}). ...les W. | authorlink = Charles W. Curtis | title=Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer | url=https://books.google.com/book ...

In [[mathematics]], the '''''n''! conjecture''' is the [[conjecture]] that the In fact, we can obtain in this manner the [[Schur polynomial|Schur functions]], the Hall–Littlewood s ...

{{about|the area in computer science|the area in applied mathematics|Structural complexity (applied mathematics)}} [[Image:Polynomial time hierarchy.svg|250px|thumb|right|Pictorial representation of the polynomial time hierarchy. The arrows denote inclusion.]] ...

...te book|title=Fixed Point Theorems with Applications to Economics and Game Theory|last=Border|first=Kim C.|publisher=Cambridge University Press|year=1989|isb : <math>\forall x \in X: \,\,\, f(x) \in F(x) \,.</math> ...

...ization]] in the full quantum theory. Renormalization theorems are common in theories with a sufficient amount of [[supersymmetry]], usually at least 4 ...ntroduced by [[Marcus T. Grisaru]], [[Martin Rocek]] and [[Warren Siegel]] in their 1979 paper [http://www.slac.stanford.edu/spires/find/hep/www?j=NUPHA, ...

...product]] of a [[finite group|finite]] [[cyclic group]] of [[order (group theory)|order]] relatively prime to ''p'' and a [[p-group|''p''-group]]. A finite ...nduction.pdf ''Induction Theorems and Isomorphism Conjectures for K- and L-Theory''] ...

{{short description|Type of theorem in automorphic forms}} ...sform]] of a modular form. More generally a converse theorem states that a representation of an algebraic group over the adeles is automorphic whenever the L-functio ...

In [[mathematics|mathematical]] [[abstract harmonic analysis|harmonic analysis *''a''(''g'') is the element ''a'' in the Iwasawa decomposition ''g''=''nak'' ...

In [[analytic number theory]], the '''Kuznetsov trace formula''' is an extension of the [[Petersson tra ...'' formula connects [[Kloosterman sum]]s at a deep level with the spectral theory of [[automorphic form]]s. Originally this could have been stated as follows ...

{{distinguish|Riesz representation theorem|Markov–Kakutani fixed-point theorem}} {{About||more theorems that are sometimes called Riesz's theorem|Riesz theorem (disambiguation){{! ...

...hnical paper on polynomial conjoint measurement for behavioural scientists in the journal ''Psychological Review''. ...ment differs from the two attribute case discovered by Luce & Tukey (1964) in that more complex composition rules are involved. ...