t--analog of q--characters

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`Qchar' is the C program for the computation of the -analog of -characters of level fundamental representations of the quantum loop algebra associated with a a simple Lie algebra of type . -analog of -characters were introduced by myself in There is a combinatorial algorithm to compute for any simple -module. It is based on the study of perverse sheaves on graded/cyclic quiver varieties. The algorithm is roughly separted into three steps:
  1. Compute for level fundamental modules.
  2. Compute for standard modules .
  3. Compute for simple modules .
The program `Qchar' is for the step 1. The step 2 is a twisted multiplication of of level fundamental modules. The step 3 is analog of the definition of Kazhdan-Lusztig polynomials.

The accompanied program `q2c' computes the ordinary character of the restriction of the level fundamental module to the -module.


  1. Download Qchar.tgz
  2. % tar xzvf Qchar.tgz
  3. Edit Makefile according to your system.
  4. % make all
(I have compiled with `gcc'. I do not know about other C's.) For :

Required Memory

level : 120GByte

level : 2.6GByte

level : 120MByte

The most important parameters are LENMAX and MAX_NUM_TERMS.


For example, for a computation of the first level fundamental module of , we type

% ./E6 1,0,1

In general,

% ./E6 a,b,c,d,e,f,...

computes the starting

But when contains an -dominant monomial other than -highest ones, the answer is not guaranteed. Level fundamental modules are known to have no -dominant monomials other than -highest. There are various options. Just type

% ./E6

to see the usage.

To get the ordinary character from the q-character,

  1. % ./E6 -f 1,0,1 (This store the date to files.)
  2. % ./E6_q2c 1,0,1