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Stability of Bott–Samelson Classes in Algebraic Cobordism

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Schubert Calculus and Its Applications in Combinatorics and Representation Theory (ICTSC 2017)

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Abstract

In this paper, we construct stable Bott–Samelson classes in the projective limit of the algebraic cobordism rings of full flag varieties, upon an initial choice of a reduced word in a given dimension. Each stable Bott–Samelson class is represented by a bounded formal power series modulo symmetric functions in positive degree. We make some explicit computations for those power series in the case of infinitesimal cohomology. We also obtain a formula of the restriction of Bott–Samelson classes to smaller flag varieties.

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Acknowledgements

The authors would like to thank the organizers of the Schubert Calculus conference at SYSU in 2017 for providing us an excellent environment for the discussions on the topic of this paper. This research was conducted in the framework of the research training group GRK 2240: Algebro-Geometric Methods in Algebra, Arithmetic and Topology, which is funded by the DFG. The second author is supported by JSPS Grant-in-Aid for Young Scientists (B) 16K17584.

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Authors and Affiliations

  1. Fachgruppe Mathematik und Informatik, Bergische Universität Wuppertal, 42119, Wuppertal, Germany

    Thomas Hudson

  2. Department of Applied Mathematics, Okayama University of Science, Okayama, 700-0005, Japan

    Tomoo Matsumura

  3. Laboratoire de Mathématiques de Versailles, CNRS, UVSQ, Université Paris–Saclay, 78000, Versailles, France

    Nicolas Perrin

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  1. Thomas Hudson
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  2. Tomoo Matsumura
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  3. Nicolas Perrin
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Corresponding author

Correspondence to Tomoo Matsumura .

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Editors and Affiliations

  1. School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong, China

    Jianxun Hu

  2. School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong, China

    Changzheng Li

  3. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Leonardo C. Mihalcea

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Hudson, T., Matsumura, T., Perrin, N. (2020). Stability of Bott–Samelson Classes in Algebraic Cobordism. In: Hu, J., Li, C., Mihalcea, L.C. (eds) Schubert Calculus and Its Applications in Combinatorics and Representation Theory. ICTSC 2017. Springer Proceedings in Mathematics & Statistics, vol 332. Springer, Singapore. https://doi.org/10.1007/978-981-15-7451-1_11

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