MackeyFunctor< rank_t > Class Template Reference

A Mackey Functor. More...

#include <MackeyFunctor.hpp>

Public Member Functions
std::string	print () const
	Prints a Mackey functor ignoring the name. More...
void	resize (int)
	Resize all member variables. More...
	MackeyFunctor ()=default
	Default constructor. More...
	MackeyFunctor (const rank_t &, int)
	When there is only one generator at each level we can use this convenient constructor More...
bool	operator== (const MackeyFunctor< rank_t > &) const
	Compares two Mackey and returns 1 if equal. More...
MackeyFunctor< rank_t >	apply (const iso_t< rank_t > &, const iso_t< rank_t > &) const
	Applies given isomorphism to Mackey functor (the inverse of the isomorphism must also be provided) More...
std::pair< std::vector< iso_t< rank_t > >, std::vector< iso_t< rank_t > > >	automorphisms () const
	Returns all automorphisms of a Mackey Functor and their inverses. More...
std::vector< MackeyFunctor< rank_t > >	isomorphism_class () const
	Returns the isomorphism class of a Mackey Functor. More...
bool	isomorphic (const std::vector< MackeyFunctor< rank_t >> &isoclass) const
	Returns 1 if the Mackey functor belongs to the provided isomorphism class. More...
bool	isomorphic (const MackeyFunctor< rank_t > &)
	Returns 1 if the Mackey functors are isomorphic. More...
void	notation ()
	Computes name for certain Mackey functors in our universal notation. More...

Public Attributes
std::vector< AbelianGroup< rank_t > >	Groups
	The Groups starting at level 0 (see Homology for the labeling) More...
std::vector< dense_t< rank_t > >	Tr
	The transfers from level i to level i+1. They are encoded as matrices because the levels may be noncyclic. More...
std::vector< dense_t< rank_t > >	Res
	Same as transfers, but now using restrictions. More...
std::vector< dense_t< rank_t > >	Weyl
	Same as transfers, but now using the Weyl group action. More...
std::string	name
	The name of the Mackey functor. More...

Detailed Description

template<typename rank_t>
class Mackey::MackeyFunctor< rank_t >

A Mackey Functor.

Constructor & Destructor Documentation

MackeyFunctor() [1/2]

MackeyFunctor ( )

default

Default constructor.

MackeyFunctor() [2/2]

MackeyFunctor	(	const rank_t &	,
		int
	)

When there is only one generator at each level we can use this convenient constructor

Member Function Documentation

print()

std::string print

(

)

const

Prints a Mackey functor ignoring the name.

resize()

void resize

(

int

)

Resize all member variables.

operator==()

bool operator==

(

const MackeyFunctor< rank_t > &

)

const

Compares two Mackey and returns 1 if equal.

apply()

MackeyFunctor<rank_t> apply	(	const iso_t< rank_t > &	,
		const iso_t< rank_t > &
	)		const

Applies given isomorphism to Mackey functor (the inverse of the isomorphism must also be provided)

automorphisms()

std::pair<std::vector<iso_t<rank_t> >, std::vector<iso_t<rank_t> > > automorphisms

(

)

const

Returns all automorphisms of a Mackey Functor and their inverses.

isomorphism_class()

std::vector<MackeyFunctor<rank_t> > isomorphism_class

(

)

const

Returns the isomorphism class of a Mackey Functor.

isomorphic() [1/2]

bool isomorphic

(

const std::vector< MackeyFunctor< rank_t >> &

isoclass

)

const

Returns 1 if the Mackey functor belongs to the provided isomorphism class.

isomorphic() [2/2]

bool isomorphic

(

const MackeyFunctor< rank_t > &

)

Returns 1 if the Mackey functors are isomorphic.

notation()

void notation

(

)

Computes name for certain Mackey functors in our universal notation.

Eg 124 means groups Z, Z/2, Z/4 bottom to top, with transfers multiplication by 2 and restrictions multiplication by 1. Eg 112 #012 means groups Z, Z, Z/2 bottom to top, with transfers multiplication by 1 and restrictions multiplication by 2 (the sharp signifies restriction and transfer swap)

Member Data Documentation

Groups

std::vector<AbelianGroup<rank_t> > Groups

The Groups starting at level 0 (see Homology for the labeling)

Tr

std::vector<dense_t<rank_t> > Tr

The transfers from level i to level i+1. They are encoded as matrices because the levels may be noncyclic.

Example (C4): If Tr[0]=[2] and Tr[1]=[1,2;1,3] then Tr_0^2(gen)=2*gen and Tr_2^4(gen0)=gen0+gen1 and Tr_2^4(gen1)=2*gen0+3*gen1

Res

std::vector<dense_t<rank_t> > Res

Same as transfers, but now using restrictions.

Weyl

std::vector<dense_t<rank_t> > Weyl

Same as transfers, but now using the Weyl group action.

name

std::string name

The name of the Mackey functor.

---

The documentation for this class was generated from the following file:

• MackeyFunctor.hpp