Lectures on the Orbit Method

By A. Kirillov. 2004

707 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c31900615cbabf52ed4540814176ecaa4556bc9a

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

An introduction to the tomographic picture of quantum mechanics (2009, background): “,t) = D(q,p)eitI. (44) In the general case n ≥1, the irreducible representations of WH(n) are parametrized up to a unitary equivalence by a real parameter γ[41]. Kirillov’s theory of coadjoint orbits [42] provides a natural way to construct them. In fact, 12 Kirillov’s theorem establishes that for n”
Representations of classical Lie groups and quantized free convolution (2013, background): “en Theorem 1.3 and decomposition of tensor products of representations of unitary group is provided by the semiclassical limit well-known in the representation theory, cf. [STS], [He], [GS], and also [Ki2] and references therein. Let us describe this limit in the language of Fourier transforms (or c”
The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups (2008, methodology): “This is a difficult problem in general: however, for certain classes of Lie groups there are suitable techniques (for instance the Kirillov orbit method for nilpotent Lie groups [21], or methods for semidirect products).”
Notes on the BMS group in three dimensions: I. Induced representations (2014, background): “[54]).”
Super-characters of finite unipotent groups of types B n , C n and D n (2006, background): “Kirillov in the context of nilpotent Lie groups (see [9,16]; see also [17]) and adapted to the case of finite unipotent groups by D.”
Differential Geometry and Lie Groups (2020, background): “Other “advanced” presentations can be found in Adams [3], Bröcker and tom Dieck [24], Serre [106, 105], Samelson [101], Humphreys [63], Fulton and Harris [46], and Kirillov [66].”
Progress in Mathematics (2013, methodology): “However, here we should mention that the noncommutative Fourier analysis on nilpotent Lie groups is extremely rich, with many powerful approaches available, such as Kirillov’s orbit method [Kir04], Mackey general description of the unitary dual, or the von Neumann algebra approaches of Dixmier [Dix7”
An Introduction to Lie Groups and Lie Algebras (2008, background): “This representation is called the coadjoint representation and plays an important role in representation theory: for example, for a large class of Lie algebras there is a bijection between (some) G–orbits in g∗ and finite-dimensional irreducible representations of g (see [30]).”
Edge modes of gravity. Part I. Corner potentials and charges (2020, background): “One of the main reasons behind this can be understood in terms of the Kirillov orbit method [33].”
Quantization on Nilpotent Lie Groups (2016, methodology): “As noted earlier, the graded Lie groups is a natural generality for such analysis since we can still make a full use of the Rockland operators as well as from the representation theory which is well understood e.g. by Kirillov’s orbit method [Kir04].”
Between classical and quantum (2005, background): “2m ∆ (perhaps with an additonal term proportional to the Ricci scalar R, see Landsman (1998)), where ∆ is the Laplacian, and quantization on Q = Rn is given by the Schrödinger equation (2.”