Iwahori–Hecke algebra

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  1. The \(A\)-basis of the Iwahori-Hecke algebra is the simplest basis that is invariant under the Goldman involution \(\#\), up to sign.[1]
  2. This gives a basis of the Iwahori-Hecke algebra whenever 2 is a unit in the base ring.[1]
  3. The \(A\)-basis induces a \(\ZZ / 2\ZZ\)-grading on the Iwahori-Hecke algebra.[1]
  4. The \(B\)-basis is the unique basis of the Iwahori-Hecke algebra that is invariant under the Goldman involution, up to sign, and invariant under the Kazhdan-Lusztig bar involution.[1]
  5. a corresponding Iwahori-Hecke algebra over the ring R as defined in chapter Iwahori-Hecke algebras.[2]
  6. CharTable returns the character table record of the Iwahori-Hecke algebra H .[2]
  7. This function returns the list of representations of the Iwahori-Hecke algebra H .[2]
  8. We do not have a function for the generic degrees of an Iwahori-Hecke algebra since they are not always defined (for example, if the parameters of the algebra are roots of unity).[2]
  9. In this talk, we show how to realize the pro-p-Iwahori-Hecke algebra of SL_n as a subalgebra of the pro-p-Iwahori-Hecke algebra of GL_n.[3]
  10. Constructs the Iwahori-Hecke algebra H of the given Coxeter group.[4]
  11. Let H be a Iwahori-Hecke algebra.[4]
  12. The way elements of the Iwahori-Hecke algebra are printed depends on the global variable PrintHecke which is a component of the global variable Artin-Tits braid groups).[4]
  13. This is only defined if all the parameters of the Iwahori-Hecke algebra are equal, and they are either equal to 1 or all sqrtParameters are bound.[4]
  14. T is an element of an Iwahori-Hecke algebra (expressed in any basis) and irreds is a set of irreducible characters of the algebra (given as vectors).[5]
  15. computes the values of the irreducible characters of the Iwahori-Hecke algebra HW on T_w^d.[5]
  16. T. J. Haines & A. Pettet, Formulae relating the Bernstein and Iwahori-Matsumoto presentations of an affine Hecke algebra, J. Algebra 252 (2002), 127-149.[6]
  17. IwahoriHeckeAlgebraT ( "B3" , q ); H The Iwahori Hecke Algebra of Type B3 in q,-1 over Univariate Polynomial Ring in q over Integer Ring and prefix T sage: T1 , T2 , T3 = H .[7]
  18. The Iwahori Hecke algebra associated with an affine Weyl group is called an affine Hecke algebra.[7]
  19. In this special case, the Iwahori Hecke algebra is identified with the group algebra of the Coxeter group.[7]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Iwahori-Hecke Algebras — Sage 9.2 Reference Manual: Algebras
  2. ↑ 2.0 2.1 2.2 2.3 GAP3 Manual: 92 Representations of Iwahori-Hecke algebras
  3. ↑ Hecke algebras in Number Theory and Categorification
  4. ↑ 4.0 4.1 4.2 4.3 GAP Manual: 81 Iwahori-Hecke algebras
  5. ↑ 5.0 5.1 GAP Manual: 82 Representations of Iwahori-Hecke algebras
  6. ↑ Shimura varieties with $\Gamma _1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case
  7. ↑ 7.0 7.1 7.2 Iwahori Hecke Algebras — Sage Reference Manual v4.5.1

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