The Iwahori-Hecke algebra Hn(q) is the C-algebra
generated by elements Ti for i<n with the relations:
2
T_i^2=(q-1)T_i+q for 1≤i ≤n-1,
T_iT_j=T_jT_i for |i-j|>1,
T_iT_i+1T_i =T_i+1T_iT_i+1T for 1≤i ≤n-2,
The 0-Hecke algebra is obtained by setting q=0 in these relations. Then,
the first relation becomes Ti2=-Ti. Let πi := 1+Ti.
perm(n)
for the permutations of n.
Note that this may be automatic in the near future.
HeckePi(n)
for the Hecke algebra
in the basis (πσ)σ∈ Sn with coefficient
the rational (Dom::rational
).
HeckeT(n)
for the Hecke algebra
in the basis (Tσ)σ∈ Sn with coefficient
the rational (Dom::rational
).
permutations::smallerBruhat
). Make
the conversion automatic.
Dom::ExpressionField()
. Modify the two parameterized domains
HeckePi(n)
and HeckeT(n)
so that they accept a ring for second
parameter with Dom::ExpressionField()
as default value.
trace
that compute the trace of the endomorphism
x∈Hn(0) →x e where e∈Hn(0).
radNormal
that normalize an element of Hn(0)
modulo its radical.
Alg
. The basis B of A is indexed by the element of
the domain Alg::basisIndices
. Like all combinatorial domain this domain may
have a list method which can be called by Alg::basisIndices::list
.
GetBasis
to compute a basis of an algebra or more
generally of a free module.
Generic Element
to compute a generic element;
Radical
to compute the radical of an algebra.
MuPAD Combinat, an open source algebraic combinatorics package