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Langlands Group
In mathematics, the Langlands group is a conjectural group ''L''''F'' attached to each local or global field ''F'', that satisfies properties similar to those of the Weil group. It was given that name by Robert Kottwitz. In Kottwitz's formulation, the Langlands group should be an extension of the Weil group by a compact group. When ''F'' is local archimedean, ''LF'' is the Weil group of ''F'', when ''F'' is local non-archimedean, ''LF'' is the product of the Weil group of ''F'' with SU(2). When ''F'' is global, the existence of ''LF'' is still conjectural, though James Arthur gives a conjectural description of it. The Langlands correspondence for ''F'' is a "natural" correspondence between the irreducible ''n''-dimensional complex representations of ''LF'' and, in the local case, the cuspidal automorphic representations of GL''n''(A''F''), where A''F'' denotes the adele Adele Laurie Blue Adkins (, ; born 5 May 1988), professionally kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a Set (mathematics), set and an Binary operation, operation that combines any two Element (mathematics), elements of the set to produce a third element of the set, in such a way that the operation is Associative property, associative, an identity element exists and every element has an Inverse element, inverse. These three axioms hold for Number#Main classification, number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The concept of a group and the axioms that define it were elaborated for handling, in a unified way, essential structural properties of very different mathematical entities such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry groups arise naturally in the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
