SciPost Submission Page
Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators
by Guner Muarem
Submission summary
| Submission information |
| Preprint link: |
scipost_202212_00038v2
|
| Date submitted: |
2023-01-05 12:27 |
| Submitted by: |
Muarem, Guner |
| Submitted to: |
SciPost Physics Proceedings |
| Proceedings issue: |
34th International Colloquium on Group Theoretical Methods in Physics |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
|
| Approach: |
Theoretical |
Abstract
In this paper we use the canonical complex structure $\boldsymbol{\mathbb{J}}$ on $\boldsymbol{\mathbb{R}^{2n}}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold. Moreover, we prove that the algebra of these Dirac operators is isomorphic to the Lie algebra $\boldsymbol{\mathfrak{su}(1,2)}$ which leads to the Howe dual pair $(\boldsymbol{\operatorname{U}(n)},\boldsymbol{\mathfrak{su}(1,2))}$.
Current status:
In voting
Author comments upon resubmission
I would like to thank the reviewer for carefully reviewing the paper.
List of changes
1) "As a matter of fact" is used too often, and can usually be removed (for example, remove it in the Abstract) => Adapted
2) Abstract: analogon -> analogue. => fixed
3) First line of Introduction: put the meaning of CAR just behind it (as you did for CCR) => fixed
4) Section 3.3: you use already ∂zj and ∂¯¯¯zj, but define it only in the next subsession. => moved above
5) Last paragraph of 3.4: ... with H an holomorphic function in several variables (i.e. is -> in) => fixed
6) Section 4, after the table: 2. We have three copies of ... (i.e. two -> three). => fixed
7) Sentence -3 of Section 4: Recall that these are ... (i.e. this -> these). => fixed
8) List in Section 5: replace m by n => fixed
