<p>Let <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H">
<mml:semantics>
<mml:mi>H</mml:mi>
<mml:annotation encoding="application/x-tex">H</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> be a connected reductive group over an algebraically closed field. We define a surjective map from the set <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C upper S left-parenthesis upper H right-parenthesis">
<mml:semantics>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>S</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>H</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:annotation encoding="application/x-tex">CS(H)</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> of unipotent character sheaves on <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H">
<mml:semantics>
<mml:mi>H</mml:mi>
<mml:annotation encoding="application/x-tex">H</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> (up to isomorphism) to the set of strata of <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H">
<mml:semantics>
<mml:mi>H</mml:mi>
<mml:annotation encoding="application/x-tex">H</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>. To do this we use the generalized Springer correspondence. We also give a new parametrization of <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C upper S left-parenthesis upper H right-parenthesis">
<mml:semantics>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>S</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>H</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:annotation encoding="application/x-tex">CS(H)</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> in terms of data coming from bad characteristic.</p>
[1]
Jonas Hetz.
On the generalised Springer correspondence for groups of type $E_8$
,
2022,
2207.06382.
[2]
G. Carnovale.
Lusztig’s strata are locally closed
,
2019,
Archiv der Mathematik.
[3]
G. Lusztig.
On conjugacy classes in a reductive group
,
2013,
1305.7168.
[4]
G. Lusztig,et al.
Representations of reductive groups over finite fields
,
2004
.
[5]
G. Lusztig.
Rationality properties of unipotent representations
,
2001,
math/0103232.
[6]
Toshiaki Shoji,et al.
Character sheaves and almost characters of reductive groups, II
,
1995
.
[7]
G. Lusztig.
Intersection cohomology complexes on a reductive group
,
1984
.
[8]
G. Lusztig.
Coxeter orbits and eigenspaces of Frobenius
,
1976
.
[9]
George Luztig.
Character Sheaves I
,
2003
.
[10]
N. Spaltenstein.
On the Generalized Springer Correspondence for Exceptional Groups
,
1985
.
[11]
G. Lusztig,et al.
On the Generalized Springer Correspondence for Classical Groups
,
1985
.
[12]
G. Lusztig,et al.
Representations of reductive groups over finite fields
,
1976
.