scholarly journals Irreducible Representations of the Quantum Weyl Algebra at Roots of Unity Given by Matrices

2014 ◽  
Vol 42 (5) ◽  
pp. 2156-2162 ◽  
Author(s):  
Blaise Heider ◽  
Linhong Wang
Keyword(s):  
Weyl Algebra ◽  
Irreducible Representations ◽  
Roots Of Unity ◽  
Quantum Weyl Algebra

Quantum Weyl Algebra

2004 ◽  
pp. 329-329
Author(s):  
Jian-zu Zhang ◽  
Roberto Floreanini ◽  
Steven Duplij ◽  
Steven Duplij ◽  
Dmitri Gitman ◽  
...  
Keyword(s):  
Weyl Algebra ◽  
Quantum Weyl Algebra

scholarly journals BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA

2020 ◽  
pp. 1-14
Author(s):  
GENQIANG LIU ◽  
YANG LI
Keyword(s):  
Complex Number ◽  
Full Subcategory ◽  
Weyl Algebra ◽  
Central Charge ◽  
Enveloping Algebra ◽  
Root Of Unity ◽  
Finite Dimensional ◽  
Quantum Weyl Algebra ◽  
Schrödinger Algebra

Abstract In 1996, a q-deformation of the universal enveloping algebra of the Schrödinger Lie algebra was introduced in Dobrev et al. [J. Phys. A 29 (1996) 5909–5918.]. This algebra is called the quantum Schrödinger algebra. In this paper, we study the Bernstein-Gelfand-Gelfand (BGG) category $\mathcal{O}$ for the quantum Schrödinger algebra $U_q(\mathfrak{s})$ , where q is a nonzero complex number which is not a root of unity. If the central charge $\dot z\neq 0$ , using the module $B_{\dot z}$ over the quantum Weyl algebra $H_q$ , we show that there is an equivalence between the full subcategory $\mathcal{O}[\dot Z]$ consisting of modules with the central charge $\dot z$ and the BGG category $\mathcal{O}^{(\mathfrak{sl}_2)}$ for the quantum group $U_q(\mathfrak{sl}_2)$ . In the case that $\dot z = 0$ , we study the subcategory $\mathcal{A}$ consisting of finite dimensional $U_q(\mathfrak{s})$ -modules of type 1 with zero action of Z. We directly construct an equivalence functor from $\mathcal{A}$ to the category of finite dimensional representations of an infinite quiver with some quadratic relations. As a corollary, we show that the category of finite dimensional $U_q(\mathfrak{s})$ -modules is wild.

The irreducible representations of the first weyl algebra

1992 ◽  
Vol 20 (5) ◽  
pp. 1493-1509
Author(s):  
Bruno J. Müller ◽  
ying-Lan Zhang
Keyword(s):  
Weyl Algebra ◽  
Irreducible Representations

Ap-Adic Quantum Weyl Algebra

2010 ◽  
Vol 38 (6) ◽  
pp. 2300-2310 ◽  
Author(s):  
Fana Tangara
Keyword(s):  
Weyl Algebra ◽  
Quantum Weyl Algebra

Fermionic and Bosonic Representations of the Extended Affine Lie Algebra

2002 ◽  
Vol 45 (4) ◽  
pp. 623-633 ◽  
Author(s):  
Yun Gao
Keyword(s):  
Lie Algebra ◽  
Weyl Algebra ◽  
Irreducible Representations ◽  
Affine Lie Algebra ◽  
Level 1 ◽  
Extended Affine Lie Algebra

AbstractWe construct a class of fermions (or bosons) by using a Clifford (or Weyl) algebra to get two families of irreducible representations for the extended affine Lie algebra of level (1, 0) (or (−1, 0)).

On the Character Rings of Finite Groups

1963 ◽  
Vol 15 ◽  
pp. 605-612 ◽  
Author(s):  
B. Banaschewski
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Characteristic Zero ◽  
Irreducible Representations ◽  
Roots Of Unity ◽  
Closed Field ◽  
One Dimensional ◽  
Elementary Group ◽  
A Finite Group ◽  
Character Ring

The characters of the representations of a finite group G over a field K of characteristic zero generate a ring oK(G) of functions on G, the K-character ring of G, which is readily seen to be Zϕ1 + . . . + Zϕn, where Z is the ring of rational integers and ϕ1, . . . , ϕn are the characters of the different irreducible representations of G over K. The theorem that every irreducible representation of G over an algebraically closed field Ω of characteristic zero is equivalent to a representation of G over the subfield of Ω which is generated by the g0th roots of unity (g0 the exponent of G) was proved by Brauer (4) via the theorems that(1) OΩ(G) is additively generated by the induced characters of representations of elementary subgroups of G, and(2) the irreducible representations over 12 of any elementary group are induced by one-dimensional subgroup representations (3).

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