Asymptotic expansion of the commutator of heisenberg fields with respect to finite-dimensional irreducible representations of the Lorentz group

1978 ◽  
Vol 37 (1) ◽  
pp. 874-879
Author(s):  
Yu. G. Shondin
Keyword(s):  
Asymptotic Expansion ◽  
Lorentz Group ◽  
Irreducible Representations ◽  
Finite Dimensional

scholarly journals Description of unitary representations of the group of infinite 𝑝-adic integer matrices

2021 ◽  
Vol 25 (21) ◽  
pp. 606-643
Author(s):  
Yury Neretin
Keyword(s):  
Irreducible Representation ◽  
Unitary Representations ◽  
Irreducible Representations ◽  
Infinite Matrices ◽  
Natural Topology ◽  
Content Type ◽  
Residue Ring ◽  
Finite Dimensional ◽  
Irreducible Unitary Representations

We classify irreducible unitary representations of the group of all infinite matrices over a p p -adic field ( p ≠ 2 p\ne 2 ) with integer elements equipped with a natural topology. Any irreducible representation passes through a group G L GL of infinite matrices over a residue ring modulo p k p^k . Irreducible representations of the latter group are induced from finite-dimensional representations of certain open subgroups.

The Duflo non-commutative Fourier transform for the Lorentz group

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040011
Author(s):  
Giacomo Rosati
Keyword(s):  
Fourier Transform ◽  
Phase Space ◽  
Quantum System ◽  
Lie Group ◽  
Lorentz Group ◽  
Commutative Algebra ◽  
Cotangent Bundle ◽  
Irreducible Representations ◽  
Algebra Representation

For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.

scholarly journals Finite-Dimensional Representations of Yangians in Complex Rank

2019 ◽  
Vol 2020 (20) ◽  
pp. 6967-6998 ◽  
Author(s):  
Daniil Kalinov
Keyword(s):  
Irreducible Representations ◽  
Finite Dimensional

Abstract We classify the “finite-dimensional” irreducible representations of the Yangians $Y(\mathfrak{g}\mathfrak{l}_t)$ and $Y(\mathfrak{s}\mathfrak{l}_t)$. These are associative ind-algebras in the Deligne category $\textrm{Rep}(GL_t)$, which generalize the regular Yangians $Y(\mathfrak{g}\mathfrak{l}_n)$ and $Y(\mathfrak{s}\mathfrak{l}_n)$ to complex rank. They were first defined in the paper [14]. Here we solve [14, Problem 7.2]. We work with the Deligne category $\textrm{Rep}(GL_t)$ using the ultraproduct approach introduced in [7] and [16].

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