$b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras

[2401.12814] $b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2401.12814 (math) [Submitted on 23 Jan 2024 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: $b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras Authors: Nitin K. Chidambaram , Maciej Dołęga , Kento Osuga View a PDF of the paper titled $b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras, by Nitin K. Chidambaram and 2 other authors View PDF HTML (experimental) Abstract: We show that $b$-Hurwitz numbers with a rational weight are obtained by taking an explicit limit of a Whittaker vector for the $\mathcal{W}$-algebra of type $A$. Our result is a vast generalization of several previous results that treated the monotone case, and the cases of quadratic and cubic polynomial weights. It also provides an interpretation of the associated Whittaker vector in terms of generalized branched coverings that might be of independent interest. Our result is new even in the special case $b=0$ that corresponds to classical hypergeometric Hurwitz numbers, and implies that they are governed by the topological recursion of Eynard-Orantin. This gives an independent proof of the recent result of Bychkov-Dunin-Barkowski-Kazarian-Shadrin. Comments: 40 pages, v2: minor edits, v3: improved presentation Subjects: Algebraic Geometry (math.AG) ; Mathematical Physics (math-ph); Combinatorics (math.CO); Representation Theory (math.RT) MSC classes: 14N10, 05E05, 05E16, 81R10 Cite as: arXiv:2401.12814 [math.AG] (or arXiv:2401.12814v3 [math.AG] for this version) https://doi.org/10.48550/arXiv.2401.12814 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nitin Kumar Chidambaram [ view email ] [v1] Tue, 23 Jan 2024 14:50:46 UTC (207 KB) [v2] Fri, 12 Apr 2024 19:15:40 UTC (208 KB) [v3] Tue, 14 Apr 2026 20:53:53 UTC (207 KB) Full-text links: Access Paper: View a PDF of the paper titled $b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras, by Nitin K. Chidambaram and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2024-01 Change to browse by: math math-ph math.CO math.MP math.RT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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