• Medientyp: E-Artikel
  • Titel: Certain components of Springer fibers and associated cycles for discrete series representations of 𝑆𝑈(𝑝,𝑞)
  • Beteiligte: Barchini, L.; Zierau, R.
  • Erschienen: American Mathematical Society (AMS), 2008
  • Erschienen in: Representation Theory of the American Mathematical Society, 12 (2008) 16, Seite 403-434
  • Sprache: Englisch
  • DOI: 10.1090/s1088-4165-08-00311-7
  • ISSN: 1088-4165
  • Schlagwörter: Mathematics (miscellaneous)
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: <p>An explicit geometric description of certain components of Springer fibers for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper L left-parenthesis n comma upper C right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">SL(n,C)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> s given in this article. These components are associated to closed <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S left-parenthesis upper G upper L left-parenthesis p right-parenthesis times upper G upper L left-parenthesis q right-parenthesis right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>×<!-- × --></mml:mo> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">S(GL(p)\times GL(q))</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-orbits in the flag variety. The geometric results are used to compute the associated cycles of the discrete series representations of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper U left-parenthesis p comma q right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">SU(p,q)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. A discussion of an alternative, and more general, computation of associated cycles is given in the appendix.</p>
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