Abstract
We give restriction formula for stable basis of the Springer resolution and generalize it to cotangent bundles of partial flag varieties. By a limiting process, we get the restriction formula of Schubert varieties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bernšteĭn, I.N., Gel’fand, I.M., Gel’fand, S.I.: Schubert cells, and the cohomology of the spaces \(G/P\). Uspehi Mat. Nauk 28(3(171)), 3–26 (1973)
Billey, S.C.: Kostant polynomials and the cohomology ring for \(G/B\). Duke Math. J. 96(1), 205–224 (1999)
Chriss, N., Ginzburg, V.: Representation Theory and Complex Geometry. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston (2010)
Fulton, W., Andersen, D.: Equivariant cohomology in Algebraic geometry. Columbia University, Spring (2007)
Ginzburg, V.: Characteristic varieties and vanishing cycles. Invent. Math. 84(2), 327–402 (1986)
Lenart, C., Zainoulline, K.: Elliptic Schubert calculus via formal root polynomials. arXiv preprint arXiv:1408.5952
Liu, C.C.M.: Localization in Gromov–Witten theory and orbifold Gromov–Witten theory. Hand book of moduli, vol. ii. Adv. Lect. Math.(ALM) 25, (2013)
Maulik, D., Okounkov, A.: Quantum groups and quantum cohomology. arXiv preprint arXiv:1211.1287 (2012)
Nakajima, H.: Lectures on Hilbert schemes of points on surfaces. University Lecture Series, vol. 18. American Mathematical Society, Providence, RI (1999)
Nakajima, H.: More lectures on Hilbert schemes of points on surfaces. arXiv preprint arXiv:1401.6782, (2014)
Negut, A.: The \(m/n\) Pieri rule. arXiv preprint arXiv:1407.5303 (2014)
Rimányi, R., Tarasov, V., Varchenko, A.: Partial flag varieties, stable envelopes and weight functions. arXiv preprint arXiv:1212.6240 (2012)
Shenfeld, D.: Abelianization of Stable Envelopes in Symplectic Resolutions. Ph.D. thesis (2013)
Smirnov, A.: Polynomials associated with fixed points on the instanton moduli space. arXiv preprint arXiv:1404.5304 (2014)
Springer, T.A.: Linear Algebraic Groups. Modern Birkhäuser Classics, 2nd edn. Birkhäuser Boston Inc, Boston (2009)
Su, C.: Equivariant quantum cohomology of cotangent bundle of \(G/P\). Adv. Math. 289, 362–383 (2016)
Tymoczko, J.S.: Divided difference operators for partial flag varieties. arXiv preprint arXiv:0912.2545 (2009)
Acknowledgments
I wish to express my deepest thanks to my advisor Prof. Andrei Okounkov for teaching me stable basis and his patience and invaluable guidance. The author also thanks Chiu-Chu Liu, Michael McBreen, Davesh Maulik, Andrei Negut, Andrey Smirnov, Zijun Zhou, Zhengyu Zong for many stimulating conversations and emails. A lot of thanks also go to my friend Pak-Hin Lee for editing a previous version of the paper. The author would also like to thank the referee for valuable comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Su, C. Restriction formula for stable basis of the Springer resolution. Sel. Math. New Ser. 23, 497–518 (2017). https://doi.org/10.1007/s00029-016-0248-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00029-016-0248-8