Abstract
We study the maximal commutative ring of partial differential operators which includes the quantum completely integrable system defined by the quantum Toda lattice. Kostant shows that the image of the generalized Harish-Chandra homomorphism of the center of the enveloping algebra is commutative (Kostant in Invent. Math. 48:101-184, 1978). We demonstrate the commutativity of the ring of partial differential operators whose principal symbols are N-invariant. Our commutative ring includes the commutative system of Kostant (Invent. Math. 48:101-184, 1978). The main tools in this paper are Fourier integral operators and Radon transforms.
| Original language | English |
|---|---|
| Pages (from-to) | 80-100 |
| Number of pages | 21 |
| Journal | Journal of Fourier Analysis and Applications |
| Volume | 15 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2009 Feb |
Fingerprint
Keywords
- Algebraic integrability
- Quantum completely integrable systems
- Radon transform
- Toda lattice
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Analysis
Cite this
The algebraic integrability of the quantum toda lattice and the radon transform. / Ikeda, Kaoru.
In: Journal of Fourier Analysis and Applications, Vol. 15, No. 1, 02.2009, p. 80-100.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The algebraic integrability of the quantum toda lattice and the radon transform
AU - Ikeda, Kaoru
PY - 2009/2
Y1 - 2009/2
N2 - We study the maximal commutative ring of partial differential operators which includes the quantum completely integrable system defined by the quantum Toda lattice. Kostant shows that the image of the generalized Harish-Chandra homomorphism of the center of the enveloping algebra is commutative (Kostant in Invent. Math. 48:101-184, 1978). We demonstrate the commutativity of the ring of partial differential operators whose principal symbols are N-invariant. Our commutative ring includes the commutative system of Kostant (Invent. Math. 48:101-184, 1978). The main tools in this paper are Fourier integral operators and Radon transforms.
AB - We study the maximal commutative ring of partial differential operators which includes the quantum completely integrable system defined by the quantum Toda lattice. Kostant shows that the image of the generalized Harish-Chandra homomorphism of the center of the enveloping algebra is commutative (Kostant in Invent. Math. 48:101-184, 1978). We demonstrate the commutativity of the ring of partial differential operators whose principal symbols are N-invariant. Our commutative ring includes the commutative system of Kostant (Invent. Math. 48:101-184, 1978). The main tools in this paper are Fourier integral operators and Radon transforms.
KW - Algebraic integrability
KW - Quantum completely integrable systems
KW - Radon transform
KW - Toda lattice
UR - http://www.scopus.com/inward/record.url?scp=62949178504&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=62949178504&partnerID=8YFLogxK
U2 - 10.1007/s00041-008-9048-7
DO - 10.1007/s00041-008-9048-7
M3 - Article
VL - 15
SP - 80
EP - 100
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
SN - 1069-5869
IS - 1
ER -