Geodesic
Vanishing Cycles and Hermitian Duality
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Monodromy in problems of algebraic geometry and differential equations, Tome 238 (2002), pp. 204-223

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We show the compatibility between the moderate nearby or vanishing cycle functor for regular holonomic $\mathcal D$-modules, as defined by Beilinson, Kashiwara, and Malgrange, and the Hermitian duality functor, as defined by Kashiwara. 
@article{TM_2002_238_a11,
     author = {C. Sabbah},
     title = {Vanishing {Cycles} and {Hermitian} {Duality}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {204--223},
     publisher = {mathdoc},
     volume = {238},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_238_a11/}
}
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C. Sabbah. Vanishing Cycles and Hermitian Duality. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Monodromy in problems of algebraic geometry and differential equations, Tome 238 (2002), pp. 204-223. http://geodesic.mathdoc.fr/item/TM_2002_238_a11/