{"issue":"3","publisher":"Princeton University Press","main_file_link":[{"url":"http://arxiv.org/abs/1204.2375","open_access":"1"}],"publist_id":"5754","author":[{"first_name":"Tamas","full_name":"Tamas Hausel","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Letellier","full_name":"Letellier, Emmanuel","first_name":"Emmanuel"},{"last_name":"Rodríguez Villegas","full_name":"Rodríguez Villegas, Fernando","first_name":"Fernando"}],"month":"01","publication_status":"published","intvolume":"       177","oa":1,"acknowledgement":"The first author thanks the Royal Society for funding his research 2005-2012 in the form of a Royal Society University Research Fellowship as well as the Mathematical Institute and Wadham College in Oxford for a very productive environment. The second author is supported by Agence Nationale de la Recherche grant\nANR-09-JCJC-0102-01. The third author is supported by the NSF grant DMS-1101484 and a Research Scholarship from the Clay Mathematical Institute.","quality_controlled":0,"title":"Positivity for Kac polynomials and DT-invariants of quivers","doi":"10.4007/annals.2013.177.3.8","date_updated":"2021-01-12T06:50:47Z","page":"1147 - 1168","date_created":"2018-12-11T11:52:02Z","date_published":"2013-01-01T00:00:00Z","abstract":[{"lang":"eng","text":"We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of Kontsevich-Soibelman. Thisis achieved by computing, via an arithmetic Fourier transform, the dimensions of the isotypical components of the cohomology of associated Nakajima quiver varieties under the action of a Weyl group. The generating function of the corresponding Poincare polynomials is an extension of Hua's formula for Kac polynomials of quivers involving Hall-Littlewood symmetric functions. The resulting formulae contain a wide range of information on the geometry of the quiver varieties."}],"_id":"1442","publication":"Annals of Mathematics","status":"public","year":"2013","extern":1,"volume":177,"day":"01","citation":{"ama":"Hausel T, Letellier E, Rodríguez Villegas F. Positivity for Kac polynomials and DT-invariants of quivers. <i>Annals of Mathematics</i>. 2013;177(3):1147-1168. doi:<a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">10.4007/annals.2013.177.3.8</a>","short":"T. Hausel, E. Letellier, F. Rodríguez Villegas, Annals of Mathematics 177 (2013) 1147–1168.","mla":"Hausel, Tamás, et al. “Positivity for Kac Polynomials and DT-Invariants of Quivers.” <i>Annals of Mathematics</i>, vol. 177, no. 3, Princeton University Press, 2013, pp. 1147–68, doi:<a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">10.4007/annals.2013.177.3.8</a>.","ieee":"T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Positivity for Kac polynomials and DT-invariants of quivers,” <i>Annals of Mathematics</i>, vol. 177, no. 3. Princeton University Press, pp. 1147–1168, 2013.","chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Positivity for Kac Polynomials and DT-Invariants of Quivers.” <i>Annals of Mathematics</i>. Princeton University Press, 2013. <a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">https://doi.org/10.4007/annals.2013.177.3.8</a>.","ista":"Hausel T, Letellier E, Rodríguez Villegas F. 2013. Positivity for Kac polynomials and DT-invariants of quivers. Annals of Mathematics. 177(3), 1147–1168.","apa":"Hausel, T., Letellier, E., &#38; Rodríguez Villegas, F. (2013). Positivity for Kac polynomials and DT-invariants of quivers. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">https://doi.org/10.4007/annals.2013.177.3.8</a>"},"type":"journal_article"}