On Wronskians and $qq$-systems - INSPIRE

DataBETA

On Wronskians and $qq$ -systems

Anton M. Zeitlin
(
- Louisiana State U., Math. Dept.
)

Aug 16, 2022

13 pages

e-Print:

2208.08018 [math.AG]

View in:

ADS Abstract Service

reference search3 citations

Citations per year

Abstract: (arXiv)

We discuss the

qq

-systems, the functional form of the Bethe ansatz equations for the twisted Gaudin model from a new geometric point of view. We use a concept of

G

-Wronskians, which are certain meromorphic sections of principal

G

-bundles on the projective line. In this context, the

qq

-system, similar to its difference analog, is realized as the relation between generalized minors of the

G

-Wronskian. We explain the link between

G

-Wronskians and twisted

G

-oper connections, which are the traditional source for the

qq

-systems.

Note:

13 pages. arXiv admin note: text overlap with arXiv:2112.02711, arXiv:2108.04184

twist
Gaudin model
Bethe ansatz

References(33)

Figures(0)

[AO]

Quasimap counts and Bethe eigenfunctions

Mina Aganagic
(
- Unlisted
)
,
Andrei Okounkov
(
- Unlisted
)

- Moscow Math.J. 17 (2017) 4, 565-600
•
e-Print:
- 1704.08746

[B1]

Exactly solved models in statistical mechanics

R.J. Baxter

[B2]

On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain

H. Bethe

- Z.Phys. 71 (1931) 205-226
•
DOI:
- 10.1007/BF01341708

[BD]

Opers

A. Beilinson
,
V. Drinfeld

•
e-Print:
- math/0501398

[BLZ]

Integrable structure of conformal field theory. 3. The Yang-Baxter relation

- Commun.Math.Phys. 200 (1999) 297-324
•
e-Print:
- hep-th/9805008
•
DOI:
- 10.1007/s002200050531

[BSZ]

Opers on the projective line, Wronskian relations, and the Bethe Ansatz

- J.Geom.Phys. 202 (2024) 105222
•
e-Print:
- 2112.02711
•
DOI:
- 10.1016/j.geomphys.2024.105222

[CG]

Representation Theory and Complex Geometry, Birkhäuser Boston, Inc., Boston, MA

N. Chriss
,
V. Ginzburg

[F1]

Opers on the projective line, flag manifolds and Bethe Ansatz

Edward Frenkel
(
- UC, Berkeley, Math. Dept.
)

e-Print:
- math/0308269

[F2]

Gaudin model and opers

Edward Frenkel
(
- UC, Berkeley, Math. Dept.
)

e-Print:
- math/0407524

[F3]

Langlands correspondence for loop groups, Cambridge University Press

E. Frenkel

[FFR1]

Gaudin model, Bethe ansatz and correlation functions at the critical level

Boris Feigin
(
- Landau Inst.
)
,
Edward Frenkel
(
- Harvard U.
)
,
Nikolai Reshetikhin
(
- UC, Berkeley, Math. Dept.
)

- Commun.Math.Phys. 166 (1994) 27-62
•
e-Print:
- hep-th/9402022
•
DOI:
- 10.1007/BF02099300

[FFR2]

Opers with irregular singularity and spectra of the shift of argument subalgebra

B. Feigin
,
E. Frenkel
,
L. Rybnikov

- Duke Math.J. 155 (2010) 337-363

[FFTL]

Gaudin models with irregular singularities

- Adv.Math. 223 (2010) 873-948
•
e-Print:
- math/0612798
•
DOI:
- 10.1016/j.aim.2009.09.007

[FH1]

Baxter’s relations and spectra of quantum integrable models

- Duke Math.J. 164 (2015) 12, 2407-2460
•
e-Print:
- 1308.3444
•
DOI:
- 10.1215/00127094-3146282

[FH2]

Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers

- Commun.Math.Phys. 362 (2018) 2, 361-414
•
e-Print:
- 1606.05301
•
DOI:
- 10.1007/s00220-018-3194-9

[FHR]

Folded quantum integrable models and deformed W-algebras

- Lett.Math.Phys. 112 (2022) 4, 80
•
e-Print:
- 2110.14600
•
DOI:
- 10.1007/s11005-022-01565-8

[FKSZ]

$q$ -opers, $QQ$ -systems, and Bethe Ansatz

- J.Eur.Math.Soc. 26 (2023) 1, 355-405
•
e-Print:
- 2002.07344
•
DOI:
- 10.4171/jems/1268

[FZ1]

Double Bruhat Cells and Total Positivity

S. Fomin
,
A. Zelevinsky

- J.Am.Math.Soc. 12 (1999) 335-380
•
e-Print:
- math/9802056

[FZ2]

Recognizing Schubert Cells, J

S. Fomin
,
A. Zelevinsky

•
e-Print:
- math/9807079

[HJ]

Asymptotic representations and Drinfeld rational fractions

- Compos.Math. 148 (2012) 1593-1623
•
e-Print:
- 1104.1891
•
DOI:
- 10.1112/S0010437X12000267

[KBI]

Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press

V. Korepin
,
N. Bogoliubov
,
A. Izergin

[KPSZ]

Quantum K-theory of quiver varieties and many-body systems

- Selecta Math. 27 (2021) 5, 87
•
e-Print:
- 1705.10419
•
DOI:
- 10.1007/s00029-021-00698-3

[KSZ]

$({{\,\mathrm{\mathrm {SL}}\,}}(N),q)$ -Opers, the $q$ -Langlands Correspondence, and Quantum/Classical Duality

- Commun.Math.Phys. 381 (2021) 2, 641-672
•
e-Print:
- 1811.09937
•
DOI:
- 10.1007/s00220-020-03891-1

[KZ1]

q-opers, QQ-systems, and Bethe Ansatz II: Generalized minors

- J.Reine Angew.Math. 2023 (2023) 795, 271-296
•
e-Print:
- 2108.04184
•
DOI:
- 10.1515/crelle-2022-0084

[KZ2]

TOROIDAL q-OPERS

- J.Inst.Math.Jussieu 22 (2023) 2, 581-642,
- J. of the Inst. of Math. of Jussieu, (2021) 1-62
•
e-Print:
- 2007.11786
•
DOI:
- 10.1017/S1474748021000220

1-25 of 33
1
2
25 / page