|
|
|
|
Список литературы
|
|
| |
| 1. |
J. Ding, K. Iohara, “Generalization of Drinfeld quantum affine algebras”, Lett. Math. Phys., 41:2 (1997), 181–193 |
| 2. |
K. Miki, “A $(q,\gamma)$ analog of the $W_{1+\infty}$ algebra”, J. Math. Phys., 48:12 (2007), 123520, 35 pp. |
| 3. |
I. Burban, O. Schiffmann, “On the Hall algebra of an elliptic curve. I”, Duke Math. J., 161:7 (2012), 1171–1231, arXiv: math/0505148 |
| 4. |
B. Feigin, K. Hashizume, A. Hoshino, J. Shiraishi, S. Yanagida, “A commutative algebra on degenerate $\mathbb{CP}^1$ and Macdonald polynomials”, J. Math. Phys., 50:9 (2009), 095215, 42 pp., arXiv: 0904.2291 |
| 5. |
B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Quantum continuous $\mathfrak{gl}_\infty$: semiinfinite construction of representations”, Kyoto J. Math., 51:2 (2011), 337–364, arXiv: 1002.3100 |
| 6. |
B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Quantum continuous $\mathfrak{gl}_\infty$: tensor products of Fock modules and $\mathcal W_n$-characters”, Kyoto J. Math., 51:2 (2011), 365–392, arXiv: 1002.3113 |
| 7. |
B. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Quantum toroidal $\mathfrak{gl}_1$ algebra: plan partitions”, Kyoto J. Math., 52:3 (2012), 621–659, arXiv: 1110.5310 |
| 8. |
B. Feigin, A. Hoshino, J. Shibahara, J. Shiraishi, S. Yanagida, “Kernel function and quantum algebra”, RIMS Kokyuroku, 1689 (2010), 133–152, arXiv: 1002.2485 |
| 9. |
B. L. Feigin, A. I. Tsymbaliuk, “Equivariant $K$-theory of Hilbert schemes via shuffle algebra”, Kyoto J. Math., 51:4 (2011), 831–854, arXiv: 0904.1679 |
| 10. |
J.-E. Bourgine, M. Fukuda, Y. Matsuo, H. Zhang, R.-D. Zhu, “Coherent states in quantum $\mathcal W_{1+\infty}$ algebra and qq-character for 5d Super Yang–Mills”, Progr. Theor. Exper. Phys., 2016:12 (2016), 123B05, 41 pp., arXiv: 1606.08020 |
| 11. |
J.-E. Bourgine, M. Fukuda, K. Harada, Y. Matsuo, R.-D. Zhu, “$(p,q)$-webs of DIM representations, 5d $\mathcal N=1$ instanton partition functions and qq-characters”, JHEP, 11 (2017), 034, 50 pp., arXiv: 1703.10759 |
| 12. |
J.-E. Bourgine, M. Fukuda, Y. Matsuo, R.-D. Zhu, “Reflection states in Ding–Iohara–Miki algebra and brane-web for D-type quiver”, JHEP, 12 (2017), 015, 26 pp., arXiv: 1709.01954 |
| 13. |
L. F. Alday, D. Gaiotto, Y. Tachikawa, “Liouville correlation functions from four-dimensional gauge theories”, Lett. Math. Phys., 91:2 (2010), 167–197, arXiv: 0906.3219 |
| 14. |
N. Wyllard, “$A_{N-1}$ conformal Toda field theory correlation functions from conformal $\mathcal N=2$ SU$(N)$ quiver gauge theories”, JHEP, 11 (2009), 002, 22 pp., arXiv: 0907.2189 |
| 15. |
V. A. Alba, V. A. Fateev, A. V. Litvinov, G. M. Tarnopolskiy, “On combinatorial expansion of the conformal blocks arising from AGT conjecture”, Lett. Math. Phys., 98:1 (2011), 33–64, arXiv: 1012.1312 |
| 16. |
V. A. Fateev, A. V. Litvinov, “Integrable structure, W-symmetry and AGT relation”, JHEP, 01 (2012), 051, 39 pp., arXiv: 1109.4042 |
| 17. |
H. Awata, Y. Yamada, “Five-dimensional AGT conjecture and the deformed Virasoro algebra”, JHEP, 01 (2010), 125, 11 pp., arXiv: 0910.4431 |
| 18. |
H. Awata, Y. Yamada, “Five-dimensional AGT relation and the deformed $\beta$-ensemble”, Prog. Theor. Phys., 124:2 (2010), 227–262, arXiv: 1004.5122 |
| 19. |
A. Mironov, A. Morozov, Sh. Shakirov, A. Smirnov, “Proving AGT conjecture as HS duality: extension to five dimensions”, Nucl. Phys. B, 855:1 (2012), 128–151, arXiv: 1105.0948 |
| 20. |
Y. Zenkevich, “Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions”, JHEP, 05 (2015), 131, 22 pp., arXiv: 1412.8592 |
| 21. |
H. Awata, B. Feigin, A. Hoshino, M. Kanai, J. Shiraishi, S. Yanagida, “Notes on Ding–Iohara algebra and AGT conjecture”, RIMS Kokyuroku, 1765 (2011), 12–32, arXiv: 1106.4088 |
| 22. |
A. Negut, “The $q$-AGT–W relations via shuffle algebra”, Commun. Math. Phys., 358:1 (2018), 101–170, arXiv: 1608.08613 |
| 23. |
H. Awata, B. Feigin, J. Shiraishi, “Quantum algebraic approach to refined topological vertex”, JHEP, 03 (2012), 041, 34 pp., arXiv: 1112.6074 |
| 24. |
H. Awata, H. Kanno, T. Matsumoto, A. Mironov, A. Morozov, A. Morozov, Y. Ohkubo, Y. Zenkevich, “Explicit examples of DIM constraints for network matrix models”, JHEP, 07 (2016), 103, 66 pp., arXiv: 1604.08366 |
| 25. |
H. Awata, H. Kanno, A. Mironov, A. Morozov, A. Morozov, Y. Ohkubo, Y. Zenkevich, “Generalized Knizhnik–Zamolodchikov equation for Ding–Iohara–Miki algebra”, Phys. Rev. D, 96:2 (2017), 026021, 19 pp., arXiv: 1703.06084 |
| 26. |
H. Awata, H. Kanno, A. Mironov, A. Morozov, A. Morozov, Y. Ohkubo, Y. Zenkevich, “Toric Calabi–Yau threefolds as quantum integrable systems. $\mathcal R$-matrix and $\mathcal{RTT}$ relations”, JHEP, 10 (2016), 047, 48 pp., arXiv: 1608.05351 |
| 27. |
H. Awata, H. Kanno, A. Mironov, A. Morozov, A. Morozov, Y. Ohkubo, Y. Zenkevich, “Anomaly in $\mathcal{RTT}$ relation for DIM algebra and network matrix models”, Nucl. Phys. B, 918 (2017), 358–385, arXiv: 1611.07304 |
| 28. |
B. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Quantum toroidal $\mathfrak{gl}_1$ and Bethe ansatz”, J. Phys. A, 48:24 (2015), 244001, 27 pp., arXiv: 1502.07194 |
| 29. |
M. Fukuda, K. Harada, Y. Matsuo, R.-D. Zhu, “Maulik–Okounkov's R-matrix from Ding–Iohara–Miki algebra”, Progr. Theor. Exp. Phys., 2017:9 (2017), 093A01, 19 pp., arXiv: 1705.02941 |
| 30. |
И. Макдональд, Симметрические функции и многочлены Холла, Мир, М., 1984 |
| 31. |
K. Mimachi, Y. Yamada, “Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials”, Commun. Math. Phys., 174:2 (1995), 447–455 |
| 32. |
K. Mimachi, Y. Yamada, “Singular vectors of Virasoro algebra in terms of Jack symmetric polynomials”, RIMS Kokyuroku, 919 (1995), 68–78 |
| 33. |
H. Awata, Y. Matsuo, S. Odake, J. Shiraishi, “Excited states of the Calogero–Sutherland model and singular vectors of the $W_N$ algebra”, Nucl. Phys. B, 449:1–2 (1995), 347–374, arXiv: hep-th/9503043 |
| 34. |
J. Shiraishi, H. Kubo, H. Awata, S. Odake, “A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions”, Lett. Math. Phys., 38:1 (1996), 33–51, arXiv: q-alg/9507034 |
| 35. |
H. Awata, H. Kubo, S. Odake, J. Shiraishi, “Quantum $\mathscr W_N$ algebras and Macdonald polynomials”, Commun. Math. Phys., 179:2 (1996), 401–416, arXiv: q-alg/9508011 |
| 36. |
H. Awata, Y. Matsuo, S. Odake, J. Shiraishi, “Collective field theory, Calogero–Sutherland model and generalized matrix models”, Phys. Lett. B, 347:1–2 (1995), 49–55, arXiv: hep-th/9411053 |
| 37. |
M. Taki, On AGT-W conjecture and $q$-deformed $W$-algebra, arXiv: 1403.7016 |
| 38. |
В. Г. Дринфельд, “Алгебры Хопфа и квантовое уравнение Янга–Бакстера”, Докл. АН СССР, 283:5 (1985), 1060–1064 |
| 39. |
В. Г. Дринфельд, “Квантовые группы”, Зап. научн. сем. ЛОМИ, 155 (1986), 18–49 |
| 40. |
M. Jimbo, “A $q$-difference analogue of $U(\mathfrak g)$ and the Yang–Baxter equation”, Lett. Math. Phys., 10:1 (1985), 63–69 |
| 41. |
B. Feigin, E. Frenkel, “Quantum $\mathscr W$ algebras and elliptic algebras”, Commun. Math. Phys., 178:3 (1996), 653–678, arXiv: q-alg/9508009 |
| 42. |
P. Bouwknegt, K. Pilch, “The deformed Virasoro algebra at roots of unity”, Commun. Math. Phys., 196:2 (1998), 249–288, arXiv: q-alg/9710026 |
| 43. |
P. Bouwknegt, K. Pilch, “On deformed $\mathcal W$-algebras and quantum affine algebras”, Adv. Theor. Math. Phys., 2:2 (1998), 357–397, arXiv: math/9801112 |
| 44. |
Y. Ohkubo, “Kac determinant and singular vector of the level $N$ representation of Ding–Iohara–Miki algebra”, Lett. Math. Phys., 109:1 (2019), 33–60, arXiv: 1706.02243 |
| 45. |
H. Awata, H. Fujino, Y. Ohkubo, “Crystallization of deformed Virasoro algebra, Ding–Iohara–Miki algebra and 5D AGT correspondence”, J. Math. Phys., 58:7 (2017), 071704, 25 pp., arXiv: 1512.08016 |
| 46. |
A. Morozov, A. Smirnov, “Towards the proof of AGT relations with the help of the generalized Jack polynomials”, Lett. Math. Phys., 104:5 (2014), 585–612, arXiv: 1307.2576 |
| 47. |
Y. Ohkubo, “Generalized Jack and Macdonald polynomials arising from AGT conjecture”, J. Phys.: Conf. Ser., 804:1 (2017), 012036, 8 pp., arXiv: 1404.5401 |
| 48. |
H. Awata, H. Kanno, “Refined BPS state counting from Nekrasov's formula and Macdonald functions”, Internat. J. Modern Phys. A, 24:12 (2009), 2253–2306, arXiv: 0805.0191 |
| 49. |
A. Iqbal, C. Kozcaz, C. Vafa, “The refined topological vertex”, JHEP, 10 (2009), 069, 58 pp., arXiv: hep-th/0701156 |
| 50. |
H. Awata, H. Kanno, A. Mironov, A. Morozov, K. Suetake, Y. Zenkevich, “$(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces”, JHEP, 03 (2018), 192, 68 pp., arXiv: 1712.08016 |
| 51. |
S. Yanagida, Norm of the Whittaker vector of the deformed Virasoro algebra, arXiv: 1411.0462 |
| 52. |
S. Yanagida, “Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state”, J. Math. Phys., 51:12 (2010), 123506, 13 pp., arXiv: 1005.0216 |
| 53. |
K. W. J. Kadell, “The Selberg–Jack symmetric functions”, Adv. Math., 130:1 (1997), 33–102 |
| 54. |
K. W. J. Kadell, “An integral for the product of two Selberg–Jack symmetric polynomials”, Compos. Math., 87:1 (1993), 5–43 |
| 55. |
J. Kaneko, “$q$-Selberg integrals and Macdonald polynomials”, Ann. Sci. École Norm. Sup. Sér. 4, 29:5 (1996), 583–637 |
| 56. |
M. Fukuda, S. Nakamura, Y. Matsuo, R.-D. Zhu, “SH${}^c$ realization of minimal model CFT: triality, poset and Burge condition”, JHEP, 11 (2015), 168, 37 pp., arXiv: 1509.01000 |